This paper considers a Bayesian approach to replacement policy model with minimal repair. We use the criterion based on the expected cost and the expected downtime to determine the optimal replacement period. To do so, we obtain the expected cost rate per unit time and the expected downtime per unit time, respectively. When the failure time is Weibull distribution with uncertain parameters, a Bayesian approach is established to formally express and update the uncertain parameters for determining an optimal maintenance policy. Especially, the overall value function suggested by Jiagn and Ji(2002) is applied to obtain the optimal replacement period. The numerical examples are presented for illustrative purpose.