Pattern-Based Bayesian model is one of the solutions for the classification problem in data mining. Most pattern-based Bayesian classifiers consider the supports of patterns in the dataset of the home class only. However, the supports of the patterns in the counterpart class are ignored. In addition, for the high-speed dynamic changes and infinite data stream, pattern-based Bayesian classifier which aims at static datasets can not work. To overcome these problems, EPDS (Bayesian classifier algorithm based on emerging pattern for data stream) is proposed. EPDS is a Bayesian classification model based on the emerging patterns discovered over data stream. In this model, EPDS presents a simple hybrid forests (HYF) data structure to maintain the itemsets of the transactions in memory, and uses a fast pattern extracting mechanism to accelerate the algorithm. EPDS adopts partially-lazy learning strategy to update emerging itemsets continuously, and establishes a local classification model in each class for the test transaction. Experimental results on real and synthetic data streams show that EPDS achieves higher classification accuracy compared to other classic classifiers.