Scene text recognition has been a hot topic in computer vision. Recent methods adopt the attention mechanism for sequence prediction which achieve convincing results. However, we argue that the existing attention mechanism faces the problem of attention diffusion, in which the model may not focus on a certain character area. In this paper, we propose Gaussian Constrained Attention Network to deal with this problem. It is a 2D attention-based method integrated with a novel Gaussian Constrained Refinement Module, which predicts an additional Gaussian mask to refine the attention weights. Different from adopting an additional supervision on the attention weights simply, our proposed method introduce an explicit refinement. In this way, the attention weights will be more concentrated and the attention-based recognition network achieves better performance. The proposed Gaussian Constrained Refinement Module is flexible and can be applied to existing attention-based methods directly. The experiments on several benchmark datasets demonstrate the effectiveness of our proposed method. Our code has been available at https://github.com/Pay20Y/GCAN.