The Student's-t mixture model, which is heavily tailed and more robust than the Gaussian mixture model, has recently received great attention on image processing. In this paper, we propose a robust non-rigid point set registration algorithm using the Student's-t mixture model. Specifically, first, we consider the alignment of two point sets as a probability density estimation problem and treat one point set as Student's-t mixture model centroids. Then, we fit the Student's-t mixture model centroids to the other point set which is treated as data. Finally, we get the closed-form solutions of registration parameters, leading to a computationally efficient registration algorithm. The proposed algorithm is especially effective for addressing the non-rigid point set registration problem when significant amounts of noise and outliers are present. Moreover, less registration parameters have to be set manually for our algorithm compared to the popular coherent points drift (CPD) algorithm. We have compared our algorithm with other state-of-the-art registration algorithms on both 2D and 3D data with noise and outliers, where our non-rigid registration algorithm showed accurate results and outperformed the other algorithms.