This article is concerned with the selection of a generative model for supervised classification. Classical model selection criteria are assessing the fit of a model rather than its ability to produce a low classification error rate. A new criterion, the so called Bayesian Entropy Criterion (BEC) is proposed. This criterion is taking into account the decisional purpose of a model by minimizing the integrated classification entropy. It provides an interesting alternative to the cross validated error rate which is highly time consuming. The asymptotic behavior of BEC criterion is presented. Numerical experiments on both simulated and real data sets show that BEC is performing better than BIC criterion to select a model minimizing the classification error rate and is providing analogous performances than the cross validated error rate.