Point cloud completion refers to the process for reconstructing a complete 3D model using incomplete point cloud data. Most of the existing point cloud completion methods are limited by the point cloud disorder and irregularity, which makes it difficult to reconstruct the local detail information, thus affecting the completion accuracy. To solve this problem, an attention-based multi-stage network for point cloud completion is proposed. A pyramid feature extractor that satisfies the replacement invariance is designed to establish the dependence between points within a localization as well as the correlation between different localizations, so as to enhance the extraction of local information while extracting global feature information. In the point cloud reconstruction process, a coarse-to-fine completion method is adopted to first generate a low-resolution seed point cloud, and then gradually enrich the local details of the seed point cloud to obtain a finer and denser point cloud. Comparison results of the experiments conducted on the public dataset PCN demonstrate that the proposed network can effectively reconstruct the local detail information, and improves the completion accuracy by at least 5.98% over the existing methods. The ablation experimental results also further validate the effectiveness of the designed attention module.