NB (Naive Bayes) classifier is a simple and effective classification method，which is based on Bayes theorem.However，its attribute conditional independence assumption usually doesn’t correspond to reality，which affects its classification performance.BAN (Bayesian network Augmented Naive Bayes) classifier extends the ability to represent the dependence among attributes.However，BAN learning algorithms need a large amount of high dimensional computations，which impairs the classification accuracy of BAN，especially on small sample datasets.Based on the variant of max-relevance min-redundancy feature selection technology，a new restrictive BAN classifier learning algorithm (k-BAN)，which builds the dependence by selecting the set of edges for each attribute node，is proposed.Compared with NB，TAN and BAN classifiers by an experiment，the restrictive BAN classifier of our algorithm has better classification accuracy，especially on small sample datasets.