In recent years, the powerful modeling ability of Graph Neural Networks (GNNs) has led to their widespread use in knowledge-aware recommender systems. However, existing GNN-based methods for information propagation among entities in knowledge graphs (KGs) may not efficiently filter out less informative entities. To address this challenge and improve the encoding of high-order structure information among many entities, we propose an end-to-end neural network-based method called Multi-stream Graph Attention Network (MSGAT). MSGAT explicitly discriminates the importance of entities from four critical perspectives and recursively propagates neighbor embeddings to refine the target node. Specifically, we use an attention mechanism from the user's perspective to distill the domain nodes' information of the predicted item in the KG, enhance the user's information on items, and generate the feature representation of the predicted item. We also propose a multi-stream attention mechanism to aggregate user history click item's neighborhood entity information in the KG and generate the user's feature representation. We conduct extensive experiments on three real datasets for movies, music, and books, and the empirical results demonstrate that MSGAT outperforms current state-of-the-art baselines.