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Predicting future motion based on historical motion sequence is a fundamental problem in computer vision, and it has wide applications in autonomous driving and robotics. Some recent works have shown that Graph Convolutional Networks(GCN) are instrumental in modeling the relationship between different joints. However, considering the variants and diverse action types in human motion data, the cross-dependency of the spatio-temporal relationships will be difficult to depict due to the decoupled modeling strategy, which may also exacerbate the problem of insufficient generalization. Therefore, we propose the Spatio-Temporal Gating-Adjacency GCN(GAGCN) to learn the complex spatio-temporal dependencies over diverse action types. Specifically, we adopt gating networks to enhance the generalization of GCN via the trainable adaptive adjacency matrix obtained by blending the candidate spatio-temporal adjacency matrices. Moreover, GAGCN addresses the cross-dependency of space and time by balancing the weights of spatio-temporal modeling and fusing the decoupled spatio-temporal features. Extensive experiments on Human 3.6M, AMASS, and 3DPW demonstrate that GAGCN achieves state-of-the-art performance in both short-term and long-term predictions.