In real applications, obtained depth images are incomplete; therefore, depth image inpainting is studied here. A novel model that is characterised by both a low-rank structure and nonlocal self-similarity is proposed. As a double constraint, the low-rank structure and nonlocal self-similarity can fully exploit the features of single-depth images to complete the inpainting task. First, according to the characteristics of pixel values, we divide the image into blocks, and similar block groups and three-dimensional arrangements are then formed. Then, the variable splitting technique is applied to effectively divide the inpainting problem into the sub-problems of the low-rank constraint and nonlocal self-similarity constraint. Finally, different strategies are used to solve different sub-problems, resulting in greater reliability. Experiments show that the proposed algorithm attains state-of-the-art performance.