This paper introduces a novel design for a robotic leg to achieve a fast running mechanism that is inspired by domestic cats. The skeletomuscular system and parallel leg movement of a cat are analyzed and applied to determine the link parameters and the linkage structure of the proposed mechanism. The linkage design of the leg mechanism is explained, and a kinematic analysis based on vector loop equations is performed. The effectiveness of the proposed mechanism is verified experimentally. A single leg clamped to a vertically moving slider exhibits a step frequency of 4.45Hz while supporting a 0.5kg body weight. The biped robot runs at an average speed of 0.75m/s at a step frequency of 2.8Hz for a trot gait on flat ground. This leg mechanism can facilitate the development of fast running robot systems.