We propose an analytic moment-based filter for nonlinear stochastic dynamical systems modeled by Gaussian processes. Exact expressions for the expected value and the covariance matrix are provided for both the prediction and the filter step, where an additional Gaussian assumption is exploited in the latter case. The new filter does not require further approximations. In particular, it avoids sample approximations. We compare the filter to a variety of available Gaussian filters, such as the EKF, the UKF, and the GP-UKF recently proposed by Ko et al. (2007).