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Classification is an important task in the field of machine learning. Most classifiers based on offline learning are invalid for open data streams. In contrast, incremental learning is feasible for continuous data. This paper presents the Incremental Bayesian Classifier “Incremental_BC”, which continuously updates the probabilistic information according to each new training sample via recursive calculation. Further, the Incremental_BC is improved to deal with the flowing data whose distribution and property evolve with time, i.e., the concept drift. The effectiveness of the proposed methods has been verified by the results of simulation tests on benchmark data sets.