Human Motion Prediction is a challenging computer vision task. First of all, the motion capture data sets are high-dimensional. Secondly, the complicated motions are often reflect multi-modal. Recently, a Gaussian process dynamic model (GPDM) [J. M. Wang, D. J. Fleet and A. Hertzmann, NIPS 2005] has been proposed for human motion tracking. In GPDM, Gaussian processes (GPs) are used to construct the nonlinear mapping in both transition and likelihood equations of the state space model. The latent states and GP hyper-parameters can then be efficiently learned from the closed-form posterior by using gradient-based optimization. In this presentation, I will mainly focus on this GPDM model, and then propose an extension of GPDM to capture the complicated motions.