The log-rank test is the most powerful nonparametric test for detecting a proportional hazards alternative; and thus, is the most commonly used procedure for analyzing time-to-event data in clinical trials. When the log-rank is used for data analysis, the power calculation should also be based on the log-rank test (Schoenfeld, 1983 Biometrics). In some clinical trials, treatment may not manifest its effect right after patients receive the treatment. Therefore, the proportional hazards assumption may not hold. We derive formulas for the asymptotic power calculation for the log-rank test under this non-proportional hazards alternative. Simulation studies indicate that the formulas provide reasonable sample sizes for a variety of trial settings. An example will be used to illustrate our methods.