The Bayesian approach to realibility acceptance sampling plan(ASP) has several advantages over the non-Bayesian approach. For instance, the former usually requires less amount of testing time and smaller sample size than the latter to demonstrate reliability. In this study, a Bayesian ASP based on a failure-free period life test is developed under the assumption of exponential lifetime distribution, and is compared with the corresponding Bayesian hybrid ASP and non-Bayesian failure-free period ASP in terms of the expected test time. It is found that the non-Bayesian failure-free period ASP has much longer expected test time than the proposed Bayesian ASP. Futher, the proposed ASP has smaller expected test time than the Bayesian hybrid ASP when the mean value of the prior distribution is large relative to the specified mean life time in the null hypothesis.