Owing to the ability of the attention mechanism to dynamically model complex node interactions, graph transformers have garnered growing interest in graph representation learning. However, due to the complexity of the attention mechanism, existing graph transformers for large-scale graph scenarios often sacrifice accurate modeling of graph topological structures. Therefore, how to capture local neighborhood and global topological structure information in graph transformers remains an urgent challenge. To address this challenge, this paper proposes a graph transformer that incorporates a local mixed filter, a graph learning model that dynamically adapts to graph homophily and efficiently models both local and global topologies. Specifically, a node-wise mixed filter is designed and applied on each subgraph to obtain local features of nodes, and a spatially-decaying graph transformer is devised to encode global topological dependencies for obtaining nodes’ global features. Furthermore, a joint training strategy is employed to facilitate the model in generating expressive and topology-aware node representations. Extensive experiments on various graph structures demonstrate the effectiveness of the proposed model.