With the popularity of stereo cameras in computer assisted surgery techniques, a second viewpoint would provide additional information in surgery. However, how to effectively access and use stereo information for the super-resolution (SR) purpose is often a challenge. In this paper, we propose a disparity-constrained stereo super-resolution network (DCSSRnet) to simultaneously compute a super-resolved image in a stereo image pair. In particular, we incorporate a disparity-based constraint mechanism into the generation of SR images in a deep neural network framework with an additional atrous parallax-attention modules. Experiment results on laparoscopic images demonstrate that the proposed framework outperforms current SR methods on both quantitative and qualitative evaluations. Our DCSSRnet provides a promising solution on enhancing spatial resolution of stereo image pairs, which will be extremely beneficial for the endoscopic surgery.