In many applications, however, the covariate is not measured exactly, but is subject to measurement error of some degree, often substantial. Thus, instead of observing the true covariate, we observe a surrogate measure. In the internal validation design, there is a subsample of individuals with a measurement on both the true covariate and the surrogate. We develop a new method for covariate error correction in the Cox survival regression model, given a modest sample of internal validation data. Unlike most previous methods for this setting, our method can handle covariate error of arbitrary form. Asymptotic properties of the estimator are derived. In a simulation study, the method was found to perform very well in terms of bias reduction and confidence interval coverage. The method is applied to data from Health Professionals Follow-Up Study on the effect of diet on incidence of Type II diabetes.