A case-cohort study is a two-phase study where at the first phase a representative sample, referred to as the study cohort, is selected from the target population. At the second phase, a subsample is selected from the study cohort based on the case status. All cases are included in the subsample whereas only a random sample of controls is included. The endpoint of interest in such studies is usually the failure time. Several methods have been proposed to estimate the relative risk or hazard ratio from a case-cohort study. Many of these methods disregard the covariate information that is not included in the sampled study sub-cohort, and therefore, results in the loss of efficiency. While there have been attempts to derive the most efficient estimators, the resulting estimators are not easily implemented from the data analysis point of view. We propose a locally efficient estimator (LEE) based on Robins et al. (1994, J. AM Stat. Assoc. 89, 846-866) by restricting the estimator to a class of regular asymptotically linear estimators. The properties of this estimator are investigated through simulations, and application to the Wilm’s tumor study.