This paper describes the dynamic analysis of the vertical jumping motion of a one-legged jumping robot that consists of a hip, a thigh, a shin, and a foot. The jumping robot has two kinds of pneumatic artificial muscles, the mono-articular muscle and the bi-articular muscle. The jumping robot is difficult to obtain the output force of each artificial muscle because each joint force is produced by the plural pneumatic artificial muscles. When the robot jumps, the forces can be projected to the waist. Thus, we developed a method that can calculate the magnitude and direction of the resultant of the forces, and convert the resultant force to the output force of the pneumatic muscles. Vertical jumping simulations are conducted, and the effectiveness of the mathematical modeling is verified.