When an experimental therapy is less extensive, less toxic, or less expensive than a standard therapy, we may want to prove that the former is not worse than the latter through a noninferiority trial. In this article, we discuss a modification of the log-rank test for noninferiority trials with survival endpoint and propose a sample size formula that can be used in designing such trials. Performance of our sample size formula is investigated through simulations. Our formula is applied to design a real clinical trial.