Weather forecasting is closely related to our daily life and has become one of the important application domains of machine learning. However, existing methods often suffer from certain problems. First, by only considering spatial proximity, the graph structure may limit the ability of model to fully capture spatial dependencies. Second, most methods typically model temporal and spatial correlations separately, which substantially limit the representational capacity of the models. Third, most methods lack the simultaneous capture of long-term and short-term temporal dependencies, which constrains the model’s capability of capturing the dynamic temporal dependency. In this work, we propose a model based on spatial-temporal fusion graphs and self-attention mechanisms, which we refer to as STGATAM. Specifically, STGATAM first constructs a novel static spatial adjacency matrix, then constructs a spatial-temporal fusion graph through the method of time step concatenation, and also constructs the corresponding spatial-temporal fusion graph adjacency matrix. We then utilize a self-attention mechanism to capture temporal dependencies, and use a graph attention network to respectively capture spatial and spatial-temporal dependencies, inputting the fused features into a decoder for prediction. We conduct multiple experiments on a real-world dataset, and the experimental results demonstrate that the method we propose significantly outperforms existing methods.