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This paper deals with the motion control and dynamics modeling of an amphibious biomimetic robot capable of multi-mode motion. A robust gait control for steady swimming using a central pattern generator (CPG) is proposed and has been successfully applied to the robot, with coordinated movements of a pair of pectoral fins and multiple modular fish-like propelling units. Combined with the hydrodynamic forces acting on the robot, a dynamics modeling based on the Lagrangian function has been established. Then some simulations are conducted with the CPG control imported into the model. By varying the input drive of the CPG model, different activities of swimming mode can be induced with the velocity, direction and type of gaits modulated accordingly. Physical tests verify the feasibility of the dynamics model coupling of the CPG control for efficient propulsion.