This paper proposes a new method to up-sample low resolution depth map for high quality and high resolution. Range sensor such as ToF camera yields low resolution depth map and the output includes heavy noise at the edges of object. Recently, many techniques have been proposed to up-sample low resolution depth map. However, there is no effective countermeasure to consider the edge noise problem in earnest. On the other hand, our proposed depth map upsampling method based on Markov Random Fields considers such edge noise characteristics of range sensors. For this reason, we newly design confidence weights for up-sampled results to be robust to the edge noise. Performance of our method is evaluated by error rate and mean absolute error through comparison with the existing methods and results show that the proposed method outperforms conventional methods.