Cleaning of glass windows for buildings is a dangerous work for human. Automatic cleaning for glass windows has been, thus, expected. Authors have developed an autonomous small-sized robot which can be used for glass window's cleaning even on not fully-flat walls. There are two major ways for the motion control of the autonomous cleaning mobile robot, which are reaction-based control method and model-based control method. Efficiency of the cleaning using the reaction-based method is lower than one using the model-based method. This study aims to develop a high efficiency and high reliable glass cleaning robot. Thus, we adopt the model-based method for the control of the cleaning robot. For the efficient and reliable cleaning, the robot should follow a desired path accurately. However, the trajectory tracking on a window is not so easy because of gravity and other dynamical effects. Moreover, even if the robot follows the desired path exactly, the robot can not assure a complete cleaning of the glass window. Therefore, the paper discusses a trajectory tracking control problem on the glass window, and also proposes a novel dirt detect sensor and a motion control method to guarantee the completeness of glass window cleaning. The validity of those proposed methods is confirmed by experiments using a window cleaning robot which attracts a window by magnetic force.