Depth maps taken by the low cost Kinect sensor are often noisy and incomplete. Thus, post-processing for obtaining reliable depth maps is necessary for advanced image and video applications such as object recognition and multi-view rendering. In this paper, we propose adaptive directional filters that fill the holes and suppress the noise in depth maps. Specifically, novel filters whose window shapes are adaptively adjusted based on the edge direction of the color image are presented. Experimental results show that our method yields higher quality filtered depth maps than other existing methods, especially at the edge boundaries.