Motions of facial components convey significant information of facial expressions. Although remarkable advancement has been made, the dynamic of facial topology has not been fully exploited. In this paper, a novel facial expression recognition (FER) algorithm called Spatial Temporal Semantic Graph Network (STSGN) is proposed to automatically learn spatial and temporal patterns through end-to-end feature learning from facial topology structure. The proposed algorithm not only has greater discriminative power to capture the dynamic patterns of facial expression and stronger generalization capability to handle different variations but also higher interpretability. Experimental evaluation on two popular datasets, CK+ and Oulu-CASIA, shows that our algorithm achieves more competitive results than other state-of-the-art methods.