Current CNN-based super-resolution (SR) methods process all locations equally with computational resources being uniformly assigned in space. However, since missing details in low-resolution (LR) images mainly exist in regions of edges and textures, less computational resources are required for those flat regions. Therefore, existing CNN-based methods involve redundant computation in flat regions, which increases their computational cost and limits their applications on mobile devices. In this paper, we explore the sparsity in image SR to improve inference efficiency of SR networks. Specifically, we develop a Sparse Mask SR (SMSR) network to learn sparse masks to prune redundant computation. Within our SMSR, spatial masks learn to identify "important" regions while channel masks learn to mark redundant channels in those "unimportant" regions. Consequently, redundant computation can be accurately localized and skipped while maintaining comparable performance. It is demonstrated that our SMSR achieves state-of-the-art performance with 41%/33%/27% FLOPs being reduced for x2/3/4 SR. Code is available at: https://github.com/LongguangWang/SMSR.