Stable, quiet, and efficient propulsion methods are essential for underwater robots to complete their tasks in a complex marine environment. However, with a single propulsion method, such as propeller propulsion and bionic propulsion, it is difficult to achieve high efficiency and high mobility at the same time. Based on the advantages of the high-efficiency propulsion of a bionic undulating fin and the stable control of the propeller, an underwater robot based on the hybrid propulsion of a quadrotor and undulating fin is proposed in this paper. This paper first introduces the mechanical implementation of the underwater robot. Then, based on kinematic modeling and theoretical derivation, the underwater motion and attitude of the robot are analyzed and the 6-DOF dynamic equation of the robot is established. Finally, the underwater motion performance of the robot is verified through field experiments. The experimental results show that the robot can realize the heave motion, surge motion, and in-situ steering motion independently and can hover stably. When the undulating frequency is 6 Hz, the maximum propulsion speed of the robot can reach up to 1.2 m/s (1.5 BL/s).