This paper presents the results of a study on the optimal footpad design for vertical climbing on acrylic surfaces with various curvatures used Taguchi methods. For a climbing robot, the adhesion system plays an important role in the climbing process. Only an appropriate adhesion strength will prevent the robot from falling and allow it to climb normally. Therefore, the footpad is a significant parameter for a climbing robot and should be studied. Taguchi methods were used to obtain a robust optimal design, where the design variables were the flat tacky elastomeric shape, area, thickness, and foam thickness of the footpad. Experiments were conducted using acrylic surfaces with various curvatures. An optimized footpad was selected based on the results of the experiments and analysis, and the stability of the wall-climbing robot was verified.