PurposeThe computing power of the legged robot is not enough to perform high-frequency updates for the full-body model predictive control (MPC) of the robot, which is a common problem encountered in the gait research of the legged robot. The purpose of this paper is to propose a high-frequency MPC control method for the bounding gait of a parallel quadruped robot.Design/methodology/approachAccording to the bounding gait characteristics of the robot, the quadruped robot model is simplified to an equivalent plane bipedal model. Under the biped robot model, the forces between the robot’s feet and the ground are calculated by MPC. Then, the authors apply a proportional differential controller to distribute these forces to the four feet of the quadruped robot. The robot video can be seen at www.bilibili.com/video/BV1je4y1S7Rn.FindingsTo verify the feasibility of the controller, a prototype was made, and the controller was deployed on the actual prototype and then fully analyzed through experiments. Experiments show that the update frequency of MPC could be stabilized at 500 Hz while the robot was running in the bounding gait stably and efficiently.Originality/valueThis paper proposes a high-frequency MPC controller under the simplified model, which has a higher working efficiency and more stable control performance.