Several legged robots have been developed in recent years and proved that they are an effective transportation system on an uneven terrain. In particular, quadruped robots are regarded as a new trend in robotics due to their superior gait stability and robustness to disturbances. More recently, many robotics researchers are making their best efforts to improve the locomotion speed, as well as the stability and robustness, of quadruped robots. The high-speed locomotion creates various challenges in the development of actuators, mechanical design, and control algorithms of the robot. In this paper, a linear actuation system for the high-speed locomotion of a quadruped robot is introduced. The proposed actuator is designed based on the principle of brushed direct-current electric motor systems. For the minimal impedance and improved power capacity, the actuator is designed with dual layers of cores, which are aligned parallel to permanent magnets. The mechanical and electrical properties of the actuation system, such as back-drivability, controllability, and response time, are verified by experimental results. A robotic leg, which is the rear leg of a Cheetah-like robot, is designed with the proposed actuator, and experimental results for trajectory tracking performance are presented.