This paper presents a method to create fish-like robots with tensegrity systems and describes a prototype modeled on the body shape of the rainbow trout with a length of 400 mm and a mass of 102 g that is driven by a waterproof servomotor. The structure of the tensegrity robot consists of rigid body segments and elastic cables that represent bone/tissue and muscles of fish, respectively. This structural configuration employing the tensegrity class 2 is much simpler than other tensegrity-based underwater robots. It also allows the tuning of the mechanical stiffness, which is often said to be an important factor in fish swimming. In our robot, the body stiffness can be tuned by changing the cross-section of the cables and their pre-stretch ratio. We characterize the robot in terms of body stiffness, swimming speed, and thrust force while varying the body stiffness i.e., the cross-section of the elastic cables. The results show that the body stiffness of the robot can be designed to approximate that of the real fish and modulate its performance characteristics. The measured swimming speed of the robot is 0.23 m/s (0.58 BL/s), which is comparable to other fish robots of the same type. Strouhal number of robot 0.54 is close to that of the natural counterpart, suggesting that the presented method is an effective engineering approach to realize the swimming characteristics of real fish.