This paper presents a new tracking control scheme for an underwater vehicle-manipulator system (UVMS). The proposed task space passivity based controller is not only used to track the given desired path but also allows the use of the self-motion of the vehicle to perform power efficient trajectory because of its kinematically redundant nature. In the proposed scheme, the primary task is to track the given end-effector task space trajectory despite of the system associated with external disturbances, system uncertainties and internal noises. The secondary task as the energy savings requirement, the vehicle motion is controlled and to be aligned with the estimated underwater current orientation. The performance and effectiveness of the proposed coordinated control motion of the UVMS is demonstrated numerically and confirmed with the specified UVMS tasks. Simulation results show that the required control inputs for the given tracking task are reduced, and the UVMS can successfully track the given desired spatial trajectory.