Detection of obstacles on a plane is important for a mobile robot that moves in a living space, especially for a humanoid that falls down even with a small obstacle. In this paper, a range image sensor for detecting small obstacles on a plane is constructed using a multi-slit laser projector. The sensor consists of a commercially available laser projector and a CCD camera. It measures a relative disparity map (RDMap) whose measurement errors are not affected by the distance. From the obtained RDMap, a plane is estimated using LMedS and regions out of the plane are detected as obstacles. Experiments show that the constructed sensor can detect small obstacles such as a LAN cable with the proposed methods.