This paper presents mechanical design, fabrication and test of a biomimetic fish robot actuated by a unimorph piezoceramic actuator, LIPCA(Lightweight Piezo-Composite curved Actuator.) We have designed a linkage mechanism that can convert bending motion of the LIPCA into the caudal fin movement. This linkage system consists of a rack-pinion system and four-bar linkage. Four types of artificial caudal fins that resemble caudal fin shapes of ostraciiform subcarangiform, carangiform, and thunniform fish, respectively, are attached to the posterior part of the robotic fish. The swimming test under 300 $V_{pp}$ input with 0.6 Hz to 1.2 Hz frequency was conducted to investigate effect of tail beat frequency and shape of caudal fin on the swimming speed of the robotic fish. At the frequency of 0.9 Hz, the maximum swimming speeds of 1.632 cm/s, 1.776 cm/s, 1.612 cm/s and 1.51 cm/s were reached for fish robots with ostraciiform, subcarangiform carangiform and thunniform caudal fins, respectively. The Strouhal number, which means the ratio between unsteady force and inertia force, or a measure of thrust efficiency, was calculated in order to examine thrust performance of the present biomimetic fish robot. The calculated Strouhal numbers show that the present robotic fish does not fall into the performance range of a fast swimming robot.