Aiming at mimicking the jumping locomotion of water striders, a new continuous jumping robot on water is proposed. Compared with the horizontal rowing motion, the jumping capability of water striders is challengeable to imitate, since the impact force on water is easy to cause the sinking of the robot. In this paper, a jumping mechanism based on springs is designed to produce a large thrust for the robot to jump. The shape of supporting legs and center of gravity of the robot are carefully designed so that the robot can jump on the surface continuously and smoothly. Influences of several critical factors, including the area of supporting legs, spring stiffness and jumping angle, on jump performance are analyzed by means of dynamic simulation and experiments. The fabricated robot weighs about 10.2 g and can continuously jump on water with the maximum leap height and length of 120 mm and 410 mm, respectively.