Traditional underwater rigid robots have some shortcomings that limit their applications in the ocean. In contrast, because of their inherent flexibility, soft robots, which have gained popularity recently, offer greater adaptability, efficiency, and safety than rigid robots. Among them, the soft actuator is the core component to power the soft robot. Here, we propose a class of soft electrohydraulic bending actuators suitable for underwater robots, which realize the bending motion of the actuator by squeezing the working liquid with an electric field. The actuator consists of a silicone rubber film, polydimethylsiloxane (PDMS) films, soft electrodes, silicone oils, an acrylic frame, and a soft flipper. When a square wave voltage is applied, the actuator can generate continuous flapping motions. By mimicking Haliclystus auricula, we designed an underwater robot based on six soft electrohydraulic bending actuators and constructed a mechanical model of the robot. Additionally, a high-voltage square wave circuit board was created to achieve the robot’s untethered motions and remote control using a smart phone via WiFi. The test results show that 1 Hz was the robot’s ideal driving frequency, and the maximum horizontal swimming speed of the robot was 7.3 mm/s.