Cause convolutional neural networks are good at abstracting local features, but poor at processing global information and long-distance dependencies, which creates a bottleneck for Person Re-identification (Re-ID) model. We combines Graph Convolutional Network (GCN) with transformer to improve the representation ability of pedestrian features in video sequences. A two-stage feature extraction and fusion framework is designed to address the complex challenges in video pedestrian recognition tasks. Specifically, GCN is used to model pedestrians in video frames, The inter-local and intra-local modeling schemes are used to construct the graph structure. The dynamic characteristics and spatial dependence of pedestrians in different frames are captured through the inter-node information propagation mechanism of GCN. Then, the transformer model is introduced for global feature extraction of GCN output feature sequences, and the self-attention mechanism of transformer is utilized to effectively integrate long-distance dependency and global context information in video sequences. With the complementary advantages of GCN and transformer, our model can generate pedestrian feature representations that contain both local details and global information. Experimental results show that the proposed model achieves excellent performance on multiple video person Re-ID benchmarks, and its effectiveness and robustness are verified.