There is increasing interest in Bayesian group sequential design because of its potential to improve efficiency in clinical trials, to shorten drug development time, and to enhance statistical inference precision without undermining the clinical trial’s integrity or validity. We propose a Bayesian sequential design for clinical trials with time-to-event outcomes and use alpha spending functions to control the overall type I error rate. Bayes factor is adapted for decision-making at interim analyses. Algorithms are presented to make decision rules and to calculate power of the proposed tests. Sensitivity analysis is implemented to evaluate the impact of different choices of prior parameters on choosing critical values. The power of tests, the expected event size of the proposed design, and the quality of estimators are studied through simulations, and compared with the frequentist group sequential design. Simulations show that at fixed total number of events, the proposed design can achieve greater power and require smaller expected event size when appropriate priors are chosen, compared with the frequentist group sequential design. The feasibility of the proposed design is further illustrated on a real data set.