In this paper we study a regression calibration method for failure time regression analysis when data on some covariates are missing or mismeasured. The method estimates the missing data based on the data structure estimated from a validation data set, a random subsample of the study cohort in which covariates are always observed. Ordinary Cox (1972; Journal of the Royal Statistical Society, Series B 34, 187-220) regression is then applied to estimate the regression coefficients, using the observed covariates in the validation data set and the estimated covariates in the nonvalidation data set. The method can be easily implemented. We present the asymptotic theory of the proposed estimator. Finite sample performance is examined and compared with an estimated partial likelihood estimator and other related methods via simulation studies, where the proposed method performs well even though it is technically inconsistent. Finally, we illustrate the method with a mouse leukemia data set.