The naive Bayesian classifier can not effectively use the dependency information between attributes. At present, the efficiency of dependency extension is emphasized, which makes the classification accuracy of the extended classifier need to be improved. By using Gaussian kernel function with a smoothing parameter to estimate attribute density, the classification accuracy criterion and the greedy parent node selection of attributes are combined to extend the naive Bayesian classifier. An experiment is done by using data sets in UCI. The results show that extended classifiers have good classification accuracy.