3D shape recognition is a challenging task due to the difficulty of representing the complex structure of 3D shapes. Recently, the view-based approaches that utilize the multiple views rendered from the shape for visual information extraction and feature aggregation to generate a global shape descriptor, achieved promising performance. However, the view-based approaches commonly ignore the exploration and utilization of local information in the multiple views, which influences the effectiveness of generated features. In this paper, we design a novel Multi-view based Local Information Fusion Network (MV-LFN) for the 3D shape recognition task. The local correlation attention mechanism (LCAM) is introduced to exploit the local correlations in the feature maps for generating a more effective view descriptor. Then, we hierarchically aggregate the multi-view feature maps to generate a shape super matrix (SSM). The local information is effectively extracted and maintained during the multi-view aggregation process, and the discrimination of shape descriptors is significantly improved. We conduct comparative experiments on the ModelNet and ShapeNetCore55 databases. The experimental performances effectively validate the superiority of MV-LFN.