It remains a great challenge for a biomimetic dolphin robot to leap out of the water by reason of requirements for very high speed and exquisite motion control. In this paper, we estimate the minimum exit speed that allows the dolphin to completely leap out of the water, and for the first time, we build a self-contained leaping dolphin robot with commercially available actuators and power supply. To quantify the possible impact of the body length on the minimum exit speed during the leap, we employ a rigid bodymodel rather than a particle model to numerically evaluate the leaping process. Furthermore, a robotic prototype intended for leap motions is created, with particular emphasis on streamlining and high-thrust tail propulsive mechanism designs in conjunction with a passive control strategy for the dorsoventral propulsion. Underwater tests on the untethered dolphin robot demonstrate the effectiveness of the proposed methods and mechatronic designs. We found that the dolphin robot successfully performed leaps with a length-specific speed of over 2.3 body lengths per second, and an emergence angle ranging between 35 and 60 degrees.