To improve the inpainting quality of the damaged videos with vertical line, scratch and characters, a video inpainting algorithm is proposed based on the sparse reconstruction of surfacelet in this paper. Since it has the three-dimensional sparse characteristics with multi-scales, multi-directions and efficient tree structure, the singular surface of a video can be captured effectively by the surfacelet transform. In the proposed scheme, the global optimization objective function of the original video is constructed based on surfacelet transform and solved using the relaxation algorithm to achieve the video inpainting. The proposed algorithm makes unnecessary the complex pretreatments such as segmentation, edge detection and so on, and improves the inpainting quality of texture and structure information in the video. Experimental results show that the inpainting quality of the proposed scheme is superior to that of the existing video inpainting algorithms.