Investigational drugs for rare cancers are often approved based solely on a single-arm phase II trial that primarily evaluates response rate in Japan. Such trials typically use a fixed sample size determined on the basis of the frequentist manner. However, since predicting the speed of patient enrollment is challenging because of the disease rarity, the time needed to complete the enrollment of the fixed number of patients is prolonged in some cases. A Bayesian design without fixing the sample size is useful for single-arm phase II trials of rare cancers. However, the arbitrariness of prior distribution specifications and the frequentist operating characteristics are regulatory issues. We recently started a Bayesian single-arm phase II trial of nivolumab in patients with sarcoma for new drug application in Japan and examined the statistical rationale and design consideration. In the Bayesian design, we specify the minimum and maximum numbers of enrolled patients during the enrollment period and the prior distributions of response rates. Considering these parameters, we obtain the minimum number of responders needed for the positive conclusion of the efficacy of nivolumab for each sample size. Simulation studies demonstrated that the operating characteristics of this design would be acceptable from the frequentist view. The Bayesian design provided an adaptive decision rule for efficacy conclusion for the drug without fixing the sample size. We hope our trial's success will provide a new drug development option for rare cancers in Japan.