In this paper, a physics-based model is proposed for a biomimetic robotic fish propelled by an ionic polymer-metal composite (IPMC) actuator. Inspired by the biological fin structure, a passive plastic fin is further attached to the IPMC beam. The model incorporates both IPMC actuation dynamics and the hydrodynamics, and predicts the steady-state cruising speed of the robot under a given periodic actuation voltage. The interactions between the plastic fin and the IPMC actuator are also captured in the model. Experimental results have shown that the proposed model is able to predict the motion of robotic fish for different tail dimensions. Since most of the model parameters are expressed in terms of fundamental physical properties and geometric dimensions, the model is expected to be instrumental in optimal design of the robotic fish.