This work focuses on developing a complete non-linear dynamic model comprising entirely kinematic and hydrodynamic effects of Carangiform locomotion based on the Lagrange approach by adapting the parameters and behaviors of a real carp. In order to imitate biological features, swimming patterns of a real carp for forward, turning and up-down motions are analyzed by using the Kineova 8.20 software. The proportional optimum link lengths according to actual size, swimming speed, flapping frequency, proportional physical parameters and different swimming motions of the real carp are investigated with the designed robotic fish model. Three-dimensional (3D) locomotion is evaluated by tracking two trajectories in a MATLAB environment. A Reaching Law Control (RLC) approach for inner loop (Euler angles-speed control) and a guidance system for the outer loop (orientation control) are proposed to provide an effective closed-loop control performance. In order to illustrate the 3D performance of the proposed closed loop control system in a virtual reality platform, the designed robotic fish model is also implemented using the Virtual Reality Modeling Language (VRML). Simulation and experimental analysis show that the proposed model gives us significant key solutions to design a fish-like robotic prototype.