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 semi-parametric 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.