In survival analysis, it is of interest to appropriately select significant predictors. In this paper, we extend the AIC(C) selection procedure of Hurvich and Tsai to survival models to improve the traditional AIC for small sample sizes. A theoretical verification under a special case of the exponential distribution is provided. Simulation studies illustrate that the proposed method substantially outperforms its counterpart: AIC, in small samples, and competes it in moderate and large samples. Two real data sets are also analyzed.