Legged robots have received widespread attention in academia and engineering owing to their excellent terrain adaptability. However, most legged robots can only adapt to high-hardness environments instead of flexible environments. Expanding the motion range of legged robots to water is a promising but challenging work. Inspired by basilisk lizards which can run on water surfaces by feet, this paper proposes a bipedal robot for water running by hydrodynamics instead of buoyancy. According to the motion parameters of the basilisk lizard during water running, a single-DoF bipedal mechanism is proposed to reproduce the motion trajectory of the feet of the basilisk lizard. Scale optimization is conducted by a particle swarm optimization algorithm to determine the geometrical parameters of the mechanism. The effects of motion frequency and foot area on mechanism performance are studied and the optimal solutions are determined. A bipedal water running robot prototype was fabricated, and the experimental results show that the prototype can generate enough support for the robot running on the water by providing a maximum lift of 2.4 times its weight and reaching a horizontal forward speed range of 0.3–0.8 m/s.