The characteristics of data stream are infinite data and quick stream speed. Clustering modeling is an important method which link to the effect of clustering technology. A nice modeling method impacts on the performance of data stream mining system. In this paper put forward a model which named Compound Gaussian Mixture Model (CGMM) and the clustering algorithm of CGMM which combines classical GMM clustering algorithm. In the paper also put forward the EM algorithm based on Compound Gaussian Mixture Model with the added labeled samples and help the initial parameters to been studied. The algorithm also can find the overlap between the Gaussian distribution and then merge them. And EM is used to initialize Compound Gaussian Mixture Model clustering algorithm. Semi-supervised clustering uses some of labeled data to help clustering analysis. The experimental results demonstrate that the algorithm increases the recognition rate for samples compared with the unsupervised study and have good clustering ability. We compare the Compound Gaussian Mixture Model Clustering algorithm and Clustream algorithm. From the results, we conclude that CGMM based on clustering algorithm has higher performance than classic Clustream algorithm. And the experimental results show that the algorithm is effective to solve data stream clustering.