Fish generates thrust with a compliant fin which is known to increase the efficiency. In this paper, the performance of a robotic dolphin, the velocity and the stability, was improved using an optimal compliant caudal fin under certain oscillating frequency. Optimal compliance of the caudal fin exists that maximizes the thrust at a certain oscillating frequency. Four different compliant fins were used to find the optimal compliance of the caudal fin at a certain frequency using the half-pi phase delay condition. The swimming results show that the optimal compliant fin increases the velocity of the robotic fish. The compliance of the caudal fin was also shown to improve the stability of the robotic fish. A reactive motion at the head of the robotic dolphin causes fluctuation of the caudal fin. This phenomenon increases with the oscillating frequency. However, compliant fin reduced this fluctuation and increased the stability.