3D video services can be supported by a multi-view video plus depth (MVD) format. The MVD format is a promising approach for realizing a natural 3D scene efficiently with a small amount of data, because it can generate virtual views for arbitrary view-points at receiver sides. Many researchers have investigated relation between a texture image and its corresponding depth map in the MVD format. In this paper, we analyze their mode correlation and then propose a fast mode decision algorithm for depth image coding based on the analysis. Experimental results indicate that the proposed method drastically reduces its encoding time with negligible quality losses in both the reconstructed depth maps and the rendered synthetic texture images.