Video super-resolution (VSR) aims to utilize multiple low-resolution frames to generate a high-resolution prediction for each frame. In this process, inter- and intra-frames are the key sources for exploiting temporal and spatial information. However, there are a couple of limitations for existing VSR methods. First, optical flow is often used to establish temporal correspondence. But flow estimation itself is error-prone and affects recovery results. Second, similar patterns existing in natural images are rarely exploited for the VSR task. Motivated by these findings, we propose a temporal multi-correspondence aggregation strategy to leverage similar patches across frames, and a cross-scale nonlocal-correspondence aggregation scheme to explore self-similarity of images across scales. Based on these two new modules, we build an effective multi-correspondence aggregation network (MuCAN) for VSR. Our method achieves state-of-the-art results on multiple benchmark datasets. Extensive experiments justify the effectiveness of our method.