Despite its unrealistic independence assumption, the Naive Bayes classifier is remarkably successful in practice. In the Naive Bayes classifier, all variables are assumed to be nominal variables, it means that each variable has a finite number of values. But in large databases, the variables often take continuous values or have a large number of numerical values. So many researchers discussed the discretization (or partitioning) for domain of the continuous variables. In this paper we generalize the Naive Bayes classifier to the situation in which the fuzzy partitioning for the variable domains instead of discretization is taken. Therefore each variable in the Fuzzy Naive Bayes classifier can take a linguistic value represented by a fuzzy set. One method for estimating the conditional probabilities in the Fuzzy Naive Bayes classifier is proposed. This generalization can decrease the complexity for learning optimal discretization, and increase the power for dealing with imprecise data and the large databases. Some well-known classification problems in machine learning field have been tested, the results show that the Fuzzy Naive Bayes classifier is an effective tool to deal with classification problem which has continuous variables.