Kinematic analysis of leaping motions can provide meaningful insights into unraveling the efficient and agile propulsive mechanisms in dolphin swimming. However, undisturbed kinematic examination of live dolphins has been very scarce due to the restriction of close-up biological observation with a motion capture system. The main objective of this study is to quantify the leaping motion of a self-propelled bionic robotic dolphin using a combined numerical and experimental method. More specifically, a dynamic model was established for the hydrodynamic analysis of a changeable submerged portion, and experimental data were then employed to identify hydrodynamic parameters and validate the effectiveness. The effects of wave-making resistance were explored, indicating that there is a varying nonlinear relationship between power and speed at different depths. In addition, the wave-making resistance can be reduced significantly when swimming at a certain depth, which leads to a higher speed and less consumed power. Quantitative estimation of leaping motion is carried out, and the results suggest that with increase of the exiting velocity and angle, the maximum height of the center of mass (CM) increases as well; furthermore, a small exiting angle usually requires a much larger exiting velocity to achieve a complete exiting motion. These findings provide implications for optimizing motion performance, which is an integral part of underwater operations in complex aquatic environments.