Natural underwater species outperform man-made underwater vehicles in many aspects. In this work, as our first effort to eventually mimic flying fish, a robotic fish capable of swimming fast and leaping out of water was developed, named KUFish. The thrust of KUFish was produced by a tail-beating mechanism driven by a DC motor in combination with reduction gears, four-bar linkage, and pulley-string mechanisms. The passive dynamic stability was implemented by the symmetric mass distribution, positive buoyancy, and lower center of gravity. A series of swimming experiments indicated that the KUFish could swim 0.68 m and leap out of the water with a speed of 1.35 m/s (6.1 BL/s) at an instant of 0.68 s after release. In addition to experimentation, a two-dimensional dynamic model was developed to predict the swimming behavior of the robot. The proposed dynamic model could reasonably capture the measured swimming performance of the robot before water leaping. The water leaping capability of the KUFish can be well supported by the computed Froude number of (1.08 or 0.92) in terms of the body faring length or robot length, respectively. The results from the current work can be useful for developing a flying-fish-like swimming robot in the future.