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The authors propose the design and control of a biologically-inspired biomimetic robotic fish capable of three-dimensional locomotion. The mechanical configuration and the hardware system of the robotic fish are described. The control architecture of the robotic fish is constructed based on central pattern generator (CPG). A model for a system of coupled non-linear oscillators is established to construct CPG and has been successfully applied to the four-link robotic fish. The CPGs are modeled as non-linear oscillators for joints and inter-joint coordination is achieved by altering the connection weights between joints. Coordinated gait patterns of rhythmic movements for swimming can be produced by modulating simple control parameters in the CPG model. The CPG-based method shows elegant and smooth transitions between swimming gaits, and enhanced ability to cope with transient perturbations because of non-linear characteristic. A series of swimming tests are designed to give speed evaluation and turning maneuver analysis. The effectiveness of the proposed method is confirmed via simulation and some experimental results.