Gait recognition has received widespread attention due to its non-intrusive recognition mechanism. Currently, most gait recognition methods use appearance-based recognition methods, and such methods are easily affected by occlusions when facing complex environments, which in turn affects the recognition accuracy. With the maturity of pose estimation techniques, model-based gait recognition methods have received more and more attention due to their robustness in complex environments. However, the current model-based gait recognition methods mainly focus on modeling the global feature information in the spatial dimension, ignoring the importance of local features and their influence on recognition accuracy. Meanwhile, in the temporal dimension, these methods usually use single-scale temporal information extraction, which does not take into account the inconsistency of the motion cycles of the limbs when a human body is walking (e.g., arm swing and leg pace), leading to the loss of some limb temporal information. To solve these problems, we propose a gait recognition network based on a Global–Local Graph Convolutional Network, called GaitMGL. Specifically, we introduce a new spatio-temporal feature extraction module, MGL (Multi-scale Temporal and Global–Local Spatial Extraction Module), which consists of GLGCN (Global–Local Graph Convolutional Network) and MTCN (Multi-scale Temporal Convolutional Network). GLGCN models both global and local features, and extracts global–local motion information. MTCN, on the other hand, takes into account the inconsistency of local limb motion cycles, and facilitates multi-scale temporal convolution to capture the temporal information of limb motion. In short, our GaitMGL solves the problems of loss of local information and loss of temporal information at a single scale that exist in existing model-based gait recognition networks. We evaluated our method on three publicly available datasets, CASIA-B, Gait3D, and GREW, and the experimental results show that our method demonstrates surprising performance and achieves an accuracy of 63.12% in the dataset GREW, exceeding all existing model-based gait recognition networks.