To deal with the low resolution of depth images and blurring depth discontinuities， a depth image super-resolution method based on shape-adaptive non-local regression and non-local gradient regularization was proposed. To explore the correlation between non-local similar patches of depth image， a shape-adaptive non-local regression method was proposed. The shape-adaptive self-similarity patch was extracted for each pixel， and a similar pixel group for the target pixel was constructed according to its shape-adaptive patch. Then for each pixel in the similar pixel group， a non-local weight was obtained with the assistant of the high-resolution color image of the same scene， thereby constructing the non-local regression prior. To maintain the edge information of the depth image， the non-locality of the gradient of the depth image was explored. Different from the Total Variation （TV） regularization which assumed that all pixels obeyed Laplacian distribution with zero mean value， through non-local similarity of the depth image， the gradient mean value of specific pixel was estimated by non-local patches， and the gradient distribution of each pixel was fit by using the learned mean value. Experimental results show that compared with Edge Inconsistency Evaluation Model （EIEM） on Middlebury datasets， the proposed method decreases Mean Absolute Difference （MAD） of 41.1% and 40.8% respectively.