In previous work on joint multiple point sets registration, the multiple point sets are often formulated by a Gaussian mixture model (GMM) and the registration is then cast to a clustering problem, which aims to exploit global relationships on the multiple point sets. However, local relationships on the multiple point sets are ignored in the state-of-the-art joint multiple point sets registration techniques. In this paper, the multiple point sets are assumed to be generated from a GMM. Local features of the multiple point sets, such as shape context, are proposed to infer the membership probabilities of the GMM. The problem of joint multiple point sets registration can be performed by maximum likelihood of the GMM. The parameters of GMM and registration are estimated by an expectation maximization algorithm. Comprehensive experiments demonstrate that our proposed method has better performance than the state-of-the-art methods.