Human motion variation synthesis is important for crowd simulation and interactive applications to enhance synthesis quality. In this paper, we propose a novel generative probabilistic model to synthesize variations of human motion. Our key idea is to model the conditional distribution of each joint via a multivariate Gaussian process model, namely semiparametric latent factor model (SLFM). SLFM can effectively model the correlations between degrees of freedom (DOFs) of joints rather than dealing with each DOF separately as implemented in existing methods. A detailed evaluation is performed to show that the proposed approach can effectively synthesize variations of different types of motions. Motions generated by our method show a richer variation compared with existing ones. Finally, our user study shows that the synthesized motion has a similar level of naturalness to captured human motions. Our method is best applied in computer games and animations to introduce motion variations.