In this paper, we theoretically predict and experimentally measure the thrust efficiency of a biomimetic robotic fish, which is propelled by an ionic polymer-metal composite (IPMC) actuator. A physics-based model that consists of IPMC dynamics and hydrodynamics was proposed, and simulation was conducted. In order to test the thrust performance of the robotic fish, a novel experimental apparatus was developed for hydrodynamic experiments. Under a servo towing system, the IPMC fish swam at a self-propelled speed where external force is averagely zero. Experimental results demonstrated that the theoretical model can well predict the thrust efficiency of the robotic fish. A maximum thrust efficiency of 2.3x10(-3) at 1 Hz was recorded experimentally, the maximum thrust force was 0.0253 N, recorded at 1.2 Hz, while the maximum speed was 0.021 m/s, recorded at 1.5 Hz, and a peak power of 0.36 W was recorded at 2.6 Hz. Additionally, the optimal actuation frequency for the thrust efficiency was also recorded at the maximum self-propelled speed. The present method of examining the thrust efficiency may also be applied to the studies of other types of smart material actuated underwater robots.