Towards the underactuated underwater robot, an optimal equivalent compensation control method is proposed with considerations of inherent characteristics of the Coanda-effect vectored thruster, such as actuator saturation and vectored moment coupling. Specifically, a sliding mode controller is designed based on trajectory tracking errors, and then radial basis function networks as well as extended state observers are built to estimate and compensate the actuator saturation and external disturbance. Then, the proposed method formulates the cost function in terms of underwater robot's recursive state deviation by means of the discrete dynamic equation. The equivalent moment can be obtained in the thruster reachable set such that the minimum of the cost function is achieved. The obtained equivalent moment not only satisfies vectored moment coupling of the thruster, but also can eliminate the disturbance for the underactuated robot effectively. It is proved that the proposed control method is asymptotically stable according to the Lyapunov theory. Simulation results also indicate the effectiveness and robustness of the control method when the underwater robot conducts trajectory tracking tasks.