This paper presents design of a climbing robot for inspection of glass curtain walls. The double-chamber structure enables the robot to climb over grooves on the glasses. In order to reduce the weight, both number and shape of the chambers are specially considered, and the pressure structure is optimized by FEA method. The statics models of different adsorption situations are also analyzed and deduced for the operational safety. In addition, design of the working arm and the wireless control system are introduced in detail. Finally, experiments of the robot are illustrated, including adsorption on different surfaces, vertical and horizontal groove-crossing as well as glass inspection. These experiments fully prove the theoretical analysis and demonstrate the climbing performance of the robot.