This paper presented a flexible and easily fabricated untethered underwater robot inspired by Aurelia, which is named “Au-robot”. The Au-robot is actuated by six radial fins made of shape memory alloy (SMA) artificial muscle modules, which can realize pulse jet propulsion motion. The thrust model of the Au-robot’s underwater motion is developed and analyzed. To achieve a multimodal and smooth swimming transition for the Au-robot, a control method integrating a central pattern generator (CPG) and an adaptive regulation (AR) heating strategy is provided. The experimental results demonstrate that the Au-robot, with good bionic properties in structure and movement mode, can achieve a smooth transition from low-frequency swimming to high-frequency swimming with an average maximum instantaneous velocity of 12.61 cm/s. It shows that a robot designed and fabricated with artificial muscle can imitate biological structures and movement traits more realistically and has better motor performance.