Animals improve their energy efficiency and adapt to changes in task requirements or in environmental conditions by controlling joint compliance dynamically. This work mimics fish’s propulsion using a compliant tail fin to show the power reduction while the fish propels by the tail fin. A compliance control scheme of caudal joint for a biomimetic autonomous underwater vehicle (BAUV) is presented. The scheme is based on actuators arranged antagonistically about joints. Design considerations on the hardware are presented to reduce the power consumption from actuators and emulate the underlying mechanics fish use to produce movement. Oscillation motions of the tail fin are driven by motors through springs. A state space model and a way-point tracking controller for the BAUV system are presented. A method is derived to determine the optimal spring compliance. Simulations are performed to verify the existence of the optimal joint compliance. Water tank experiments using a BAUV demonstrate that tuning joint compliances can reduce the amount of energy required for the propulsion of the tail fin.