We propose a bipedal walking and impact reduction algorithm for a bipedal robot with pneumatically driven knees. The proposed algorithm is meaningful in that unlike in the existing studies on fully pneumaticallydriven robots and their control, it can overcome the low control performance of pneumatic actuators while utilizing the high compliance of pneumatic actuators through the high control performance of other joints in robots that applypneumatic actuators only to the knee joint. Our algorithm takes advantage of whole-body control to overcome the low control performance of pneumatic systems and utilizes pneumatic compliance by simultaneously controllingthe force and stiffness of the pneumatic actuators. Since a pneumatic actuator outputs a force, a force and torque converter is added to the general whole-body control framework, and a torque limit is considered as a functionof the joint angle. In addition, a mechanism for selecting the stiffness of the knee is added. In particular, a force control method based on maintaining the minimum stiffness is applied to reduce the impact force when the groundconditions suddenly change. The pneumatics and the robot system were accurately modeled in a simulation, and the proposed algorithm was applied in the simulation to realize bipedal walking and to confirm the impact reductioneffect in the event of a sudden ground condition change.