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Facial expression recognition (FER), aiming to classify the expression present in the facial image or video, has attracted a lot of research interests in the field of artificial intelligence and multimedia. In terms of video based FER task, it is sensible to capture the dynamic expression variation among the frames to recognize facial expression. However, existing methods directly utilize CNN-RNN or 3D CNN to extract the spatial-temporal features from different facial units, instead of concentrating on a certain region during expression variation capturing, which leads to limited performance in FER. In our paper, we introduce a Graph Convolutional Network (GCN) layer into a common CNN-RNN based model for video-based FER. First, the GCN layer is utilized to learn more significant facial expression features which concentrate on certain regions after sharing information between extracted CNN features of nodes. Then, a LSTM layer is applied to learn long-term dependencies among the GCN learned features to model the variation. In addition, a weight assignment mechanism is also designed to weight the output of different nodes for final classification by characterizing the expression intensities in each frame. To the best of our knowledge, it is the first time to use GCN in FER task. We evaluate our method on three widely-used datasets, CK+, Oulu-CASIA and MMI, and also one challenging wild dataset AFEW8.0, and the experimental results demonstrate that our method has superior performance to existing methods.