Occlusion is still a severe problem in the video-based Re-IDentification (Re-ID) task, which has a great impact on the success rate. The attention mechanism has been proved to be helpful in solving the occlusion problem by a large number of existing methods. However, their attention mechanisms still lack the capability to extract sufficient discriminative information into the final representations from the videos. The single attention module scheme employed by existing methods cannot exploit multi-scale spatial cues, and the attention of the single module will be dispersed by multiple salient parts of the person. In this paper, we propose a Concentrated Multi-grained Multi-Attention Network (CMMANet) where two multi-attention modules are designed to extract multi-grained information through processing multi-scale intermediate features. Furthermore, multiple attention submodules in each multi-attention module can automatically discover multiple discriminative regions of the video frames. To achieve this goal, we introduce a diversity loss to diversify the submodules in each multi-attention module, and a concentration loss to integrate their attention responses so that each submodule can strongly focus on a specific meaningful part. The experimental results show that the proposed approach outperforms the state-of-the-art methods by large margins on multiple public datasets.