Forecasting the future plausible paths of pedestrians in crowd scenes is of wide applications, but it still remains as a challenging task due to the complexities and uncertainties of crowd motions. To address these issues, we propose to explore the inherent crowd dynamics via a social-aware recurrent Gaussian process model, which facilitates the path prediction by taking advantages of the interplay between the rich prior knowledge and motion uncertainties. Specifically, we derive a social-aware LSTM to explore the crowd dynamic, resulting in a hidden feature embedding the rich prior in massive data. Afterwards, we integrate the descriptor into deep Gaussian processes with motion uncertainties appropriately harnessed. Crowd motion forecasting is implemented by regressing relative motion against the current positions, yielding the predicted paths based on a functional object associated with a distribution. Extensive experiments on public datasets demonstrate that our method obtains the state-of-the-art performance in both structured and unstructured scenes by exploring the complex and uncertain motion patterns, even if the occlusion is serious or the observed trajectories are noisy.