This paper proposed a novel type of bionic underwater robot (BUR). The undulation and jet propulsion modes on the self-propelled BUR were combined, and the kinematic characteristics of the two propulsion modes were thoroughly compared. First, the prototype and swimming strategy of the BUR were presented, and a dynamic model of the BUR was established based on several assumptions. Then, a central pattern generator (CPG) model allowing free adjustment of frequency and amplitude was employed to achieve the undulation propulsion of carangiform fish and the jet propulsion of jellyfish. Also, the kinematic characteristics of the two propulsion modes were investigated through experiments under different caudal fin actuation parameters. The experimental results indicate that the developed prototype can realize the undulation and jet propulsion by the means of the coordinated movement of the multi-caudal fins. By adjusting the CPG parameters, the BUR can switch the propulsion mode smoothly. Furthermore, the propulsion velocity of the BUR initially increased rapidly with the frequency and then slowed down when the frequency was greater than 0.8 Hz in both propulsion modes. The undulation propulsion velocity increased with the amplitude in the measurement ranges, however, the jet propulsion velocity initially increased quickly with the amplitude and then kept constant and even decreased when the amplitude was greater than 11 cm. Under the same caudal fin actuation parameters, the average velocity in undulation propulsion mode was higher than that in jet propulsion mode.