In this paper, a new concept of a wall-climbing robot able to climb a vertical plane is presented. A continuous locomotive motion with a high climbing speed of 15m/min is realized by adopting a series chain on two tracked wheels on which 24 suction pads are installed. While each tracked wheel rotates, the suction pads which attach to the vertical plane are activated in sequence by specially designed mechanical valves. The engineering analysis and detailed mechanism design of the tracked wheel, including mechanical valves and the overall features, are described in this paper. It is a self-contained robot in which a vacuum pump and a power supply are integrated and is controlled remotely. The climbing performance, using the proposed mechanism, is evaluated on a vertical steel plate. Finally, the procedures are presented for an optimization experiment using Taguchi methodology to maximize vacuum pressure which is a critical factor for suction force.