Classification on noisy data streams has recently become one of the most important topics in streaming data mining. In this paper, a Classification algorithm for mining Data Streams based on Mixture Models of C4.5 and NB is proposed called CDSMM. In this algorithm, C4.5 is used as the base classifiers, the hypothesis testing method is introduced for the detection of concept drifts, and a Naïve Bayes classifier is adopted to filter noise. Extensive experiments demonstrate that CDSMM has substantial advantages over similar existing algorithms in the predictive accuracy on noisy data streams with concept drifts.