Stereo image super-resolution (SR) has achieved great progress in recent years. However, the existing methods are unable to obtain rich cross-view information at a low computational cost. In addition, these methods treat each pixel equally when fusing the cross-view information with the intra-view information, resulting in non-robustness of the fused information. In this work, we propose a multi-scale parallax attention stereo super-resolution network (MPASSRnet) to address these problems. Firstly, we design a multi-scale parallax attention module (MSPAM), which computes the similarity between stereo images on multiple scale images based on the introduction of pixel-to-patch matching, thus acquiring multi-scale cross-view information at a low computational cost. Second, we propose a pixel attention fusion module (PAFM), which introduces spatial attention (SA) by calculating the correlation between cross-view information and intra-view information, and combines channel attention (CA) to make the fused information more robust. Finally, extensive experiments show that our method achieves state-of-the-art performance on the benchmark datasets.