This presentation contains forward-looking statements. Such statements include, but are not limited to, statements regarding our research, preclinical and clinical development activities, plans and projected timelines fo

DEVELOPING PRECISION MEDICINES FOR THE

TREATMENT OF CANCER Corporate Presentation - December 2020 Exhibit 99.1

This presentation contains

forward-looking statements. Such statements include, but are not limited to, statements regarding our research, preclinical and clinical development activities, plans and projected timelines for tipifarnib and KO-539, plans regarding regulatory

filings, our expectations regarding the relative benefits of our product candidates versus competitive therapies, and our expectations regarding the therapeutic and commercial potential of our product candidates. The words "believe,"

"may," "will," "estimate," "promise," "plan", "continue," "anticipate," "intend," "expect," "potential" and similar expressions

(including the negative thereof), are intended to identify forward-looking statements. Because such statements are subject to risks and uncertainties, actual results may differ materially from those expressed or implied by such forward-looking

statements. Risks that contribute to the uncertain nature of the forward-looking statements include: our preclinical studies and clinical trials may not be successful; the U.S. Food and Drug Administration (FDA) may not agree with our interpretation

of the data from clinical trials of our product candidates; we may decide, or the FDA may require us, to conduct additional clinical trials or to modify our ongoing clinical trials; we may experience delays in the commencement, enrollment,

completion or analysis of clinical testing for our product candidates, or significant issues regarding the adequacy of our clinical trial designs or the execution of our clinical trials may arise, which could result in increased costs and delays, or

limit our ability to obtain regulatory approval; the commencement, enrollment and completion of clinical trials and the reporting of data therefrom; the COVID-19 pandemic may disrupt our business and that of the third parties on which we depend,

including delaying or otherwise disrupting our clinical trials and preclinical studies, manufacturing and supply chain, or impairing employee productivity; our product candidates may not receive regulatory approval or be successfully commercialized;

unexpected adverse side effects or inadequate therapeutic efficacy of our product candidates could delay or prevent regulatory approval or commercialization; and we may not be able to obtain additional financing. Additional risks and uncertainties

may emerge from time to time, and it is not possible for Kura's management to predict all risk factors and uncertainties. All forward-looking statements contained in this presentation speak only as of the date on which they were made. Other

risks and uncertainties affecting us are described more fully in our filings with the Securities and Exchange Commission. We undertake no obligation to update such statements to reflect events that occur or circumstances that exist after the date on

which they were made. Forward-Looking Statements

*Cash, cash equivalents and short-term

investments as of September 30, 2020 Targeted Oncology Advancing two wholly owned, targeted oncology drug candidates using a precision medicine approach; fast-to-market strategy Proprietary Pipeline Tipifarnib: Farnesyl transferase inhibitor

Registration-directed trial in HRAS mutant head and neck squamous cell carcinoma (HNSCC) ongoing Opportunity to expand to HRAS and PI3K dependent tumors Multiple clinical proof-of-concept studies support significant lifecycle expansion

opportunities KO-539: Menin inhibitor Potent and selective inhibitor of the menin-KMT2A(MLL) protein-protein interaction Potential to target ~35% of acute myeloid leukemia (AML) Preliminary Phase 1 data show encouraging safety, tolerability and

clinical activity in multiple genetically defined subgroups of AML Strong Financials $325.4 million in cash* provides runway into 2023 Investment Highlights

Proven oncology drug development and

commercialization expertise Kura Leadership Team and Board of Directors Leadership Team Troy Wilson, Ph.D., J.D. President & Chief Executive Officer James Basta, J.D. Chief Legal Officer Stephen Dale, M.D. Chief Medical Officer Kirsten Flowers

Chief Commercial Officer Kathleen Ford Chief Operating Officer Marc Grasso, M.D. Chief Financial Officer & Chief Business Officer Board of Directors Faheem Hasnain Executive Chairman, Gossamer Bio Robert Hoffman Former Chief Financial Officer,

Heron Therapeutics Thomas Malley President, Mossrock Capital Diane Parks Former Head of U.S. Commercial, Kite Pharma Steven Stein, M.D. Chief Medical Officer, Incyte Mary Szela President and CEO, TriSalus Life Sciences Troy Wilson, Ph.D., J.D.

President and CEO, Kura Oncology

Advancing Targeted Oncology Drug

Candidates Using a Precision Medicine Approach Targeting KMT2A(MLL)-r and NPM1-Mutant AML Orphan Drug Designation Opportunity to address large patient population with high unmet need in relapsed/refractory AML Publications support potential to drive

robust and persistent responses in KMT2A(MLL)-r and NPM1-mutant AML Targeting HRAS Mutant Solid Tumors Fast Track Designation Initial opportunity to address high unmet need in relapsed/refractory HRAS mutant HNSCC Opportunities to expand to broader

patient populations and to additional indications KO-539 Tipifarnib

TIPIFARNIB IN HRAS MUTANT SOLID

Tipifarnib in HRAS Mutant Solid Tumors

Unique MOA targets farnesylation, an essential modification required for activity of the HRAS mutant oncoprotein Phase 2 data demonstrates treatment response of ~ 50% ORR, ~ 6 months PFS and ~ 15 months OS in advanced recurrent and metastatic HRAS

mutant HNSCC patients Favorable safety and tolerability profile supports broad use in advanced patients as well as expansion to earlier therapeutic settings Fast Track Designation in HRAS Mutant HNSCC; potential for accelerated approval Novel

mechanism and well tolerated profile could enable use in combination with standard of care, including immune therapy, targeted therapies and chemo Issued and pending patents provide exclusivity to 2036 in major markets

Cell membrane HRAS HRAS FTase HRAS

FTase Tipifarnib HRAS (mutant) HRAS (wild-type) Tipifarnib inhibits farnesylation and signaling activity of the HRAS oncoprotein Farnesylation is essential for HRAS signal transduction activity HRAS mutations drive proliferation and resistance

mechanisms in solid tumors Incidence of HRAS mutations in HNSCC is approximately 4-8% and varies by region Tipifarnib Inhibits Farnesylation - An Essential Modification Required for HRAS Activity

Source: Kura internal data Tipifarnib

Tipifarnib Vehicle Vehicle Change in tumor volume (%)* HRAS wild type HRAS-mutant * Capped at 200%. Actual values 208-597% MAPK signaling Cell cycle arrest Apoptosis Angiogenesis Squamous differentiation Antitumor activity in PDX models HRAS

membrane displacement pERK Ki67 c.CSP3 CD31 KRT4 Tipifarnib Displays Robust, Selective Activity in HRAS Mutant HNSCC Models

Ho et al. AACR-NCI-EORTC 2019 #384

(preliminary data as of 10/17/19) Efficacy-evaluable patients with HRAS mutant variant allele frequency (VAF) 20% and serum albumin 3.5 g/dL, or HRAS VAF 35% One patient treated off-protocol through compassionate use RUN-HN:

Phase 2 Trial in HRAS Mutant HNSCC Time on Treatment ORR ~ 50% N=18 evaluable patients Not yet efficacy evaluable PR SD Not efficacy evaluable unconfirmed PR (uPR) 600 mg starting dose * Treatment Cycles (28 days) Durable Anti-Tumor Activity with

Tipifarnib as a Monotherapy in Patients with HRAS Mutant HNSCC

Ho et al. ASCO 2020 #6504

(preliminary data as of 9/30/19) Efficacy-evaluable patients with HRAS mutant variant allele frequency (VAF) 20% and serum albumin 3.5 g/dL, or HRAS VAF 35% One patient treated off-protocol through compassionate use

Progression-Free Survival with Tipifarnib and Last Prior Therapy in Patients with HRAS Mutant HNSCC Median PFS (months) 95% CI Lower Upper Tipifarnib HNSCC with high VAF, including additional patient (N=18) 5.9 3.5 19.2 Last prior line of therapy

(n=17) 2.8 1.1 5.2 RUN-HN: Phase 2 Trial in HRAS Mutant HNSCC

Overall Survival in Patients with

HRAS Mutant HNSCC Median OS (months) 95% CI Lower Upper HNSCC with high VAF, including additional patient (N=18) 15.4 7.0 46.4 Ho et al. ASCO 2020 #6504 (preliminary exploratory data as of 9/30/19) Efficacy-evaluable patients with HRAS mutant

variant allele frequency (VAF) 20% and serum albumin 3.5 g/dL, or HRAS VAF 35% One patient treated off-protocol through compassionate use RUN-HN: Phase 2 Trial in HRAS Mutant HNSCC

* Feedback from end-of-Phase 2

meeting with FDA 2018 AIM-HN: Registration-directed trial of tipifarnib in HRAS mutant HNSCC Recurrent or metastatic patients after one prior line of platinum therapy Now open in ~90 clinical sites in the U.S., Europe and Asia Amended trial to

enroll all HRAS mutant HNSCC patients regardless of variant allele frequency Intended to support an NDA seeking accelerated approval* SEQ-HN: Prospective observational cohort of HNSCC Matched case-control study designed to: Characterize natural

history of HRAS mutant HNSCC patients and their outcomes after first line therapy Enable identification of patients for potential enrollment into AIM-HN May support potential FDA labelling discussions, post-approval commitments and commercial

considerations Registration Strategy in HRAS Mutant HNSCC

Only ~1/3 of patients with advanced

diagnosis survive 5 years4 SURVIVORS DO NOT SURVIVE 0 20 40 60 80 100 Outcomes with currently available therapies (including I-O therapy) are poor5 1 Bray et al. CA Cancer J Clin. 2018;68(6):394-424 2 Cramer et al. Nat Rev Clin Oncol. 2019

Nov;16(11):669-683 | ACS Cancer Facts and Figures 2020 3 Siegel et al. CA Cancer J Clin. 2020;70(1):7-30 4 National Cancer Institute. Introduction to head & neck cancer. https://training.seer.cancer.gov/head-neck/intro/. Accessed March 4, 2019 5

N Engl J Med. 2008 Sep 11;359(11):1116-27 | Keytruda & Opdivo package inserts | J Clin Oncol. 2007 Jun 1;25(16):2171-7 | J Clin Oncol. 2012 30:15_suppl, 5574-5574 Tipifarnib Has the Potential to be the First Small Molecule Targeted Therapy for

HNSCC Patients OS First line: 10-15 mo Second line: 5-8 mo PFS First line: 3-5 mo Second line: 2-3 mo ORR First line: 20-36% Second line: 13-16% Head and neck squamous cell carcinoma ranks as the 7th leading cancer worldwide3 Globally, ~885,000

people develop head and neck cancer annually and ~450,000 die of HNSCC each year1 60,000+ cases of HNSCC per year in the U.S.2

Expansion Opportunities for

Tipifarnib in HRAS and pi3k dependent HNSCC

HRAS Dependent Tumors Represent a

Significant Subset of HNSCC with Distinct Biology Several independent studies cluster HRAS mutant HNSCCs as part of a larger subset1 TCGA cohort shows overexpression of HRAS gene in 25-30% of HNSCC2 Average HRAS expression in HNSCC is 5-10x higher

than in other tumor types Together with HRAS mutant tumors, HRAS-overexpressing HNSCC may represent a significant subset of HRAS dependent tumors with distinct biology that is targeted by tipifarnib HRAS Overexpressed 1 Campbell et al. (2018), Cell

Rep. 23:194; Su et al. (2017), Theranostics, 7:1088; 2 International Cancer Genome Consortium (2013), Nat. Commun.| 4:2873

HRAS is a Central Resistance

Mechanism to Other Therapies in PDX Models of HRAS Dependent HNSCC Tipifarnib displays additive or synergistic anti-tumor activity with a range of other drugs in HRAS-overexpressing patient-derived xenograft (PDX) models HRAS represents a key node

at the center of HNSCC tumor biology, driving resistance to other therapies and reinforcing the potential for combination strategies with tipifarnib 1HRAS likely drives immunosuppression in HNSCC, and tipifarnib may also sensitize to immunotherapy

via inhibition of CXCL12 production by activated carcinoma-associated fibroblasts HRAS PI3K I/O1 Chemo MAPK

Combinations of Tipifarnib and

PI3K Inhibitor Demonstrate Robust Activity in HNSCC PDX Models Malik et al. EORTC-NCI-AACR 2020 #159 Tipifarnib used at reduced dose to simulate potential lower doses in combination (80 60mg/kg BID) BYL-719 used at reduced dose to

simulate potential lower doses in combination (60 40mg/kg QD) Mean Tumor Volume SEM Days of treatment HRAS-mutant PIK3CA-mutant Wild-Type

Combinations of Tipifarnib and

PI3K inhibitors Have Broad Therapeutic Potential in HNSCC HRAS-MAPK and PI3K-mTOR are complementary pathways in HNSCC Overexpression of WT HRAS reported to induce resistance to PI3K inhibition HRAS is reported to preferentially activate

PI3K (vs. KRAS; vs. MAPK) HRAS mutation/over expression and PIK3CA mutations/amplifications account for 25-50% of HNSCC1 PIK3CA mutations/amplification: 30-40% (25% estimated overlap with HRAS overexpressing tumors) HRAS overexpression: 20-30% HRAS

mutations: 4-8% (83% overexpress HRAS) Preclinical data is supportive of the combination; enhanced activity observed in both HRAS mutant/overexpressed and PIK3CA mutant/amplified populations of HNSCC 1TCGA Data References: Yan J et al (1998) JBC

273:24052 ; Gupta S et al (2007) Cell 129:957 ; Zhao L et al (2008) PNAS 105:2652

Patents cover combinations of

tipifarnib with other agents (e.g., I/O) Additional patents possible with specific agents, doses, schedules, etc. Multiple issued U.S. patents covering biomarker-guided indications provide patent exclusivity to 2036 Additional patent applications

pending in the U.S. and foreign countries for tipifarnib in other biomarkers and disease indications U.S. patents cover use of "any farnesyl transferase inhibitor" Researching FTIs with superior properties to tipifarnib Expect

composition of matter IP on new discoveries Tipifarnib / FTI Patent Exclusivity Proprietary Biomarkers and Methods Combinations Novel FTI Program Layered patent strategy provides patent exclusivity to 2036 in major markets

KO-539: Menin Inhibitor in acute

KO-539: Menin Inhibitor Potent,

selective, reversible, oral inhibitor of menin-KMT2A(MLL) protein-protein interaction for treatment of AML Novel MOA targeting epigenetic dysregulation leading to differentiation block and anti-tumor activity in 35% or more of AML Preliminary data

from KOMET-001 Phase 1/2A dose-escalation study show encouraging safety, tolerability and clinical activity in multiple genetically defined subgroups of AML Focused monotherapy development strategy in multiple genetic subtypes: KMT2A(MLL) rearranged

(5-10% of AML) NPM1 mutant (30% of AML) Other genetic subtypes (e.g., SETD2/RUNX1-mutant AML) Potential to combine with other targeted therapies and induction chemotherapy Issued and pending COM patents provide worldwide coverage to 2036

Targeting Menin-KMT2A(MLL)

Interaction Provides Potential Therapeutic Intervention into Two Genetic Subsets of AML Targeting the menin-KMT2A(MLL) interaction to reverse epigenetic dysregulation in MLL-rearranged AML A central role for menin-KMT2A(MLL) interaction in

epigenetic dysregulation in NPM1-mutant AML K hn MW, et al. Cancer Discov. 2016;6(10):1166-1181 | Thorsteinsdottir U, et al. Mol Cell Biol. 2001;21(1):224-234 Patel SS, et al. Curr Hematol Malig Rep. 2020;15(4):350-359 | Brunetti L,

et al. Cancer Cell. 2018;34(3):499-512

Burrows et al. AACR-NCI-EORTC 2017

LB-A27 100% (10/10) of animals treated with single-agent KO-539 cleared their leukemia and became long-term survivors Tumor growth inhibition was durable - no leukemia was detectable in blood or bone marrow two months after cessation of dosing

KO-539 was well tolerated at tested dose levels Comparator compound (FLT3 inhibitor) was initially active, but all animals eventually relapsed AM7577 Overall Survival CD45+ Human AML Blasts Tolerability Last dose Last dose KO-539 Produces Lasting

Complete Remissions in a NPM1 / DNMT3A / IDH2 / FLT3-Mutant AML Model

KOMET-001: Phase 1/2A First-in-Human

Study of KO-539 in Patients with Relapsed or Refractory AML KOMET: Kura Oncology Menin-MLL Trial MLL/KMT2A-rearranged AML Cohort NPM1-mutant AML Cohort Determine recommended Phase 2 dose and/or MTD Safety and tolerability Pharmacokinetics Early