Recently, consumer depth cameras have gained significant popularity due to their affordable cost. However, the limited resolution and quality of the depth map generated by these cameras are still problems for several applications. In this paper, we propose a novel framework for single depth image super resolution guided by a high resolution edge map constructed from the edges in the low resolution depth image via a Markov Random Field (MRF) optimization. With the guidance of the high resolution edge map, the high resolution depth image is up-sampled via a joint bilateral filter. The edge guidance not only helps avoid artifacts introduced by direct texture prediction, but also reduces the jagged artifacts and preserves the sharp edges. Experimental results demonstrate the effectiveness of our proposed algorithm compared to previously reported methods.