This paper deals with the Bayesian implementation of an allocation rule in an environment with quasi-linear preferences. We analyze the implementation under the assumption that the principal does not know the prior distribution of agents' types, though the distribution is common knowledge among agents. Assuming that the agents' types are independent prior distributions, we show that an allocation rule with SSS can be fully implemented in perfect Bayesian equilibrium. However, in the case of dependent prior distribution of agents' types, we show that this result cannot hold. Hence, we suggest the sufficient condition for implementation.