This paper is concerned with the design of a robotic fish and its motion control algorithms. A radio-controlled, four-link biomimetic robotic fish is developed using a flexible posterior body and an oscillating foil as a propeller. The swimming speed of the robotic fish is adjusted by modulating joint's oscillating frequency, and its orientation is tuned by different joint's deflections. Since the motion control of a robotic fish involves both hydrodynamics of the fluid environment and dynamics of the robot, it is very difficult to establish a precise mathematical model employing purely analytical methods. Therefore, the fish's motion control task is decomposed into two control systems. The online speed control implements a hybrid control strategy and a proportional-integral-derivative (PID) control algorithm. The orientation control system is based on a fuzzy logic controller. In our experiments, a point-to-point (PTP) control algorithm is implemented and an overhead vision system is adopted to provide real-time visual feedback. The experimental results confirm the effectiveness of the proposed algorithms.