Recently, consumer depth cameras have gained significant popularity due to their affordable cost. However, the limited resolution and the quality of the depth map generated by these cameras are still problematic for several applications. In this paper, a novel framework for the single depth image superresolution is proposed. In our framework, the upscaling of a single depth image is guided by a high-resolution edge map, which is constructed from the edges of the low-resolution depth image through a Markov random field optimization in a patch synthesis based manner. We also explore the self-similarity of patches during the edge construction stage, when limited training data are available. With the guidance of the high-resolution edge map, we propose upsampling the high-resolution depth image through a modified joint bilateral filter. The edge-based guidance not only helps avoiding artifacts introduced by direct texture prediction, but also reduces jagged artifacts and preserves the sharp edges. Experimental results demonstrate the effectiveness of our method both qualitatively and quantitatively compared with the state-of-the-art methods.