The problem of evaluating the goodness of the predictive distributions of Bayesian models is investigated. To evaluate the Bayesian model, deviance information criteria (DIC) has been extensively employed in various study areas, thanks to its simplicity of calculation from the posterior output. Unfortunately, it is also true that the DIC has been criticized due to the over fitting. Inheriting the simplicity form of DIC, we propose a new criterion that overcomes the over fitting problem. Under the model misspecification situation, the proposed criterion is developed by correcting the asymptotic bias of the posterior mean of the likelihood as an estimate of its expected likelihood. The proposed criteria are robust to any improper priors. Monte Carlo simulations are conducted to investigate the properties of the proposed criteria. We also show that the proposed criteria can avoid over fitting problem.