In this paper, a new robotic fish propelled by a hybrid tail, which is actuated by two active joints, is developed. The first joint is driven by a servo motor, which generates flapping motions for main propulsion. The second joint is actuated by a soft actuator, an ionic polymer-metal composite (IPMC) artificial muscle, which directs the propelled fluid for steering. A state-space dynamic model is developed to capture the two-dimensional (2D) motion dynamics of the robotic fish. The model fully captures the actuation dynamics of the IPMC soft actuator, two-link tail motion dynamics, and body motion dynamics. Experimental results have shown that the robotic fish is capable of swimming forward (up to 0.45 body length/s) and turning left and right (up to 40 deg/s) with a small turning radius (less than half a body length). Finally, the dynamic model has been validated with experimental data, in terms of steady-state forward speed and turning speed at steady-state versus flapping frequency.