Fish locomotion which adopts body and/or caudal fin swimming mode consists of different motions, such as Cruising-straight, Cruising-turn, and various fast turns, among others. Currently, there is no single mathematical model that could illustrate all these motions. Thus, for scientists and engineers, it is quite cumbersome and complicated to model and control different motions with multiple principles. In this article, we proposed a general kinematic model to illustrate the kinematics of all aforementioned swimming motions. The model is synthesized by a nonlinear oscillator and a traveling wave equation. By changing four parameters extracted from the model, the kinematic model can demonstrate all the aforementioned swimming motions with different amplitudes and frequencies. To verify the model, we built a multijoint robotic fish and developed its dynamic model and control method to perform all the maneuvers under the guidance of the general kinematic model. Through this systematic methodology, one can easily study the principles of different swimming motions and design the multimotions controller for a robotic fish through only one governing kinematic model.