This study proposes some results in classifying by Bayesian method. There are upper and lower bounds of the Bayes error as well as its determination in case of one dimension and multidimensions. Based on the proposals for estimating of probability density functions, calculating the Bayes error and determining the prior probability, we establish an algorithm to evaluate ability of customers to pay debts at banks. This algorithm has been performed by the Matlab procedure that can be applied well with real data. The proposed algorithm is tested by the real application at a bank in Viet Nam that obtains the best results in comparing with the existing approaches.