This paper proposes a point cloud completion network based on multi-branch multi-scale feature fusion because the existing networks cannot extract high-quality global and local features of point clouds simultaneously and lose point cloud detail and coordinate information. The novelty of this network is its hierarchical progressive feature extraction and fusion mechanism. In the encoding stage, the proposed network first uses the Joint Feature Extraction Module (JFEM) to perform multi-scale feature learning using the input point cloud data of three different resolutions and successively extracts global features containing rich semantic information and fine local features to maximize the retention of key information. Subsequently, the Detail-Preserving Pooling (DP-Pool) module is used for reducing the dimensions of the features to avoid the loss of detail caused by traditional pooling operations. The multi-branch encoding structure is combined to achieve efficient fusion of global and local features, ensuring that features of different scales can complement each other. In the decoding stage, the network gradually restores the geometric structure of the point cloud via the Point Cloud Reconstruction (PCR) module, uses the multi-branch decoding structure to finely upsample the features at different levels, and generates a high-fidelity, high-density completed point cloud. Experimental results show that the performance of the proposed network is better than those of the top 10 advanced point cloud completion networks and can further improve the quality of point cloud completion.