Underwater robots are becoming increasingly important in various fields. Fish robots are attracting attention as an alternative to the screw-type robots currently in use. We developed a compact robot with a high swimming performance by mimicking the anatomical structure of fish. In this paper, we focus on the red muscles, tendons, and vertebrae used for steady swimming of fish. A robot was fabricated by replacing the red muscle structure with shape memory alloy wires and rigid body links. In our previous work, undulation motions with various phase differences and backward quadratically increasing inter-vertebral bending angles were confirmed in the air, while the swimming performance in insulating fluid was poor. To improve the swimming performance, an improved robot was designed that mimics the muscle contractions of mackerel using a pulley mechanism, with the robot named UEC Mackerel. In swimming experiments using the improved robot, a maximum swimming speed of 25.8 mm/s (0.11 BL/s) was recorded, which is comparable to that of other soft-swimming robots. In addition, the cost of transport (COT), representing the energy consumption required for robot movement, was calculated, and a minimum COT of 0.08 was recorded, which is comparable to that of an actual fish.