Depth information is a critical factor for increasing the quality of immersive media. However, depth estimation approaches still have issues in maintaining the depth continuity, and there is inconsistency between the depth edges and the corresponding color edges. The proposed algorithm aims to solve this problem. The proposed depth-estimation method uses a graph-cut on a superpixel basis. We present a novel energy function used in graph-edge weights, and add preprocessing and local depth refinement to remove superpixel noise. Simulation results demonstrate that the proposed algorithm provides a more accurate depth image, which maintains global continuity, compared to the other conventional methods.