Legged robots are regarded as a new means for transportation at uneven terrains and dangerous situations. In particular, quadruped robots that are capable of high-speed running are receiving great attention due to their superior mobility. The legs of such high-speed running robots rapidly repeat the swing and stance motions. Therefore, the legs of high-speed running robots should exhibit low impedance and friction for fast swing motions, while it is required to produce a significantly large actuation force for propulsion of the robot body in a stance phase. For this purpose, a direct-driven actuation mechanism was proposed for the Cheetaroid robot in our previous work. In this paper, in order to further enlarge the frequency bandwidth of the leg module and to reduce the required control (i.e., actuation) power, a dual-stage spring is designed to introduce a motion-adaptive resonance into the system. The structure and parameters of the dual-stage spring are determined in an optimal manner to minimize the control power. The resonance due to the dual-stage spring occurs only during highspeed locomotion, since the overall mechanism is designed such that the spring force is applied to the leg for high-speed locomotion only. The proposed system is verified by simulation studies and experimental results in this paper.