In this paper, we present a fish-like underwater robot inspired by the black bass fish. This robot is composed of a deformable structure and muscle-like linear actuators based on shape memory alloy wires. Such actuators are used to bend a continuous structure representing the backbone of the fish. The prototype is also equipped with a bio-inspired synthetic skin made of liquid silicone rubber and Lycra microfiber mesh. We present the mechatronics of the prototype and its control scheme, which take advantage of flex sensors for proprioception. Experiments under different conditions (in air and in water) assess the effectiveness of the mechatronics design and demonstrate that a relatively simple PID controller provides high precision of the muscles' position control. Here, the implementation of biomimetic kinematics and silent actuation technology in bio-inspired underwater robotics are demonstrated. Progress in this technology could provide multiple applications, including fish farming, coastal protection and live animal monitoring where silent robotics are necessary.