The obtained dynamic equations in inertial frame are highly coupled and fully nonlinear, thus those are not conductive to controller design. Inspired by Autonomous Underwater Vehicle(AUV) modeling in non-inertia frame, this paper defines the non-inertial frame that is always aligned with the eel robot. The kinematic model is derived by using Coriolis' theorem. By using improved Newton's second law and the principle of moment balance, the dynamic equations are derived, in which the hydrodynamic forces and torques take into account current effects, nonlinear drag forces, added mass forces and fluid torque effects. The established dynamic model is analytical and can be utilized in modern model-based control schemes, regardless of the number of modules. Compared with the existed model, the model established in this paper obtains the tangential velocity sub-dynamics directly and achieves the purpose of simplifying the model by the orientation angle parameter decoupling. In order to verify the accuracy of the proposed model, simulations of a eel robot with nine links are presented. Simulation results indicate the proposed model fits well with the proposed model.