In this paper, we propose a probabilistic framework for model-based clustering of direction of arrival (DOA) data to obtain stable sound source localization (SSL) estimates. Model-based clustering has been shown capable of handling highly overlapped and noisy datasets, such as those involved in DOA detection. Although the Gaussian mixture model is commonly used for model-based clustering, we propose use of the von Mises mixture model as more befitting circular DOA data than a Gaussian distribution. The EM framework for the von Mises mixture model in a unit hyper sphere is degenerated for the 2D case and used as such in the proposed method. We also use a histogram of the dataset to initialize the number of clusters and the initial values of parameters, thereby saving calculation time and improving the efficiency. Experiments using simulated and real-world datasets demonstrate the performance of the proposed method.