Video super-resolution (VSR) aims at recovering high-resolution frames from their lowresolution counterparts. Over the past few years, deep neural networks have dominated the video super-resolution task because of its strong non-linear representational ability. To exploit temporal correlations, most deep neural networks have to face two challenges: (1) how to align consecutive frames containing motions, occlusions and blurring, and establish accurate temporal correspondences, (2) how to effectively fuse aligned frames and balance their contributions. In this work, a novel video super-resolution network, named NLVSR, is proposed to solve above problems in an efficient and effective manner. For alignment, a temporal-spatial non-local operation is employed to align each frame to the reference frame. Compared with existing alignment approaches, the proposed temporalspatial non-local operation is able to integrate the global information of each frame by a weighted sum, leading to a better performance in alignment. For fusion, an attentionbased progressive fusion framework was designed to integrate aligned frames gradually. To penalize the points with low-quality in aligned features, an attention mechanism was employed for a robust reconstruction. Experimental results demonstrate the superiority of the proposed network in terms of quantitative and qualitative evaluation, and surpasses other state-of-the-art methods by 0.33 dB at least. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.