Graph Convolutional Networks (GCNs) have been widely applied and achieved significant results in skeleton-based action recognition. However, existing methods mostly focus on modeling static spatial features of the skeleton structure, while overlooking the highly coordinated temporal and spatial relationships among joints. In this work, we propose Sliding Window Attention Graph Convolution (SWAGC) method which introduces local sliding windows to expand spatial feature extraction in the temporal dimension and propagates joint features to capture key joint information in different temporal periods. Furthermore, to better model temporal dynamics, we introduce Global Multi-Scale Temporal Convolution (GMSTC). GMSTC combines multi-scale temporal convolutions with self-attention mechanism to extract global multi-scale temporal dynamics and enhance the modeling capability for different types of actions. Combining SWAGC and GMSTC, we develop a graph convolutional network named SWA-GCN, which achieves performance comparable to state-of-the-art methods on 3 main stream datasets: NTU RGB+D, NTU RGB+D 120, and NW-UCLA.