In recent years, great achievements have been made in graph convolutional network (GCN) for non-Euclidean spatial data feature extraction, especially the skeleton-based feature extraction. However, the fixed graph structure determined by the fixed adjacency matrix usually causes the problems such as the weak spatial modeling ability, the unsatisfactory generalization performance, the excessively large number of model parameters, and so on. In this paper, a spatially adaptive residual graph convolutional network (SARGCN) is proposed for action recognition based on skeleton feature extraction. Firstly, the uniform and fixed topology is not required in our graph. Secondly, a learnable parameter matrix is added to the GCN operation, which can enhance the model’s capabilities of feature extraction and generalization, while reducing the number of parameters. Therefore, compared with the several existing models mentioned in this paper, the least number of parameters are used in our model while ensuring the comparable recognition accuracy. Finally, inspired by the ResNet architecture, a residual connection is introduced in GCN to obtain higher accuracy at lower computational costs and learning difficulties. Extensive experimental on two large-scale datasets results validate the effectiveness of our proposed approach, namely NTU RGB+D 60 and NTU RGB+D 120.