The ability of forecasting future human motion is important for human-machine interaction systems to understand human behaviors and make interaction. In this work, we focus on developing models to predict future human motion from past observed video frames. Motivated by the observation that human motion is closely related to the action being performed, we propose to explore action context to guide motion prediction. Specifically, we construct an action-specific memory bank to store representative motion dynamics for each action category, and design a query-read process to retrieve some motion dynamics from the memory bank. The retrieved dynamics are consistent with the action depicted in the observed video frames and serve as a strong prior knowledge to guide motion prediction. We further formulate an action constraint loss to ensure the global semantic consistency of the predicted motion. Extensive experiments demonstrate the effectiveness of the proposed approach, and we achieve state-of-the-art performance on 3D human motion prediction.