Some large cohort studies could cost hundreds of millions of dollars. Due to the limited budget, researchers are seeking for cost-effective designs. In this paper, we consider a two-phase probability dependent sampling scheme for failure time data, where one selects a simple random sample at the first phase and targets more informative subjects based on a certain probability at the second phase. Simulation studies show that the proposed estimator outperformed two competitive estimators, one from a simple random sample of the same sample size and the other from the outcome-dependent sampling design. We also develop the optimal allocation of the subsamples for the two-phase probability dependent sampling scheme under the fixed sample size. We then apply our proposed design and estimator to the Busseltion Health Study.