In recent years, depth recovery based on deep networks has achieved great success. However, the existing state-of-the-art network designs perform like black boxes in depth recovery tasks, lacking a clear mechanism. Utilizing the property that there is a large amount of non-local common characteristics in depth images, we propose a novel model-guided depth recovery method, namely the DC-NLAR model. A non-local auto-regressive regular term is also embedded into our model to capture more non-local depth information. To fully use the excellent performance of neural networks, we develop a deep image prior to better describe the characteristic of depth images. We also introduce an implicit data consistency term to tackle the degenerate operator with high heterogeneity. We then unfold the proposed model into networks by using the half-quadratic splitting algorithm. This proposed method is experimented on the NYU-Depth V2 and SUN RGB-D datasets, and the experimental results achieve comparable performance to that of deep learning methods.