To improve the registration accuracy of three-dimensional point clouds in the complex situations of random data missing, noise interference and so on, a method of registering point clouds based on multi-dimensional mixed Cauchy distribution (MMC) is proposed. The mathematical model of point clouds is extended to the MMC model, and the parameters of this model are solved to construct a characteristic tetrahedron so that the rotation matrix and translation vector are optimized. Based on the MMC model, the data centers, covariance matrices and weights of target point clouds and point clouds to register are obtained by the expectation-maximization algorithm. The simulation data and experimental data show that the MMC algorithm can be used to realize an accurate registration and simultaneously possesses a good robustness if compared with several common algorithms under the conditions that the point cloud data are occluded, missing, size-inconsistent, interfered by random noise and out of order.