This paper studies the trajectory tracking control problem of a ship-borne manipulator system (SBMS) which comprises of a robotic manipulator installed on an unmanned surface vehicle (USV). In order to deal with external disturbances and model uncertainties in the SBMS, the composite trajectory tracking control method based on full-order terminal sliding mode (FOTSM) control is proposed. The main contributions of this paper are: (1) A dynamics model of the SBMS taking into consideration of the dynamic coupling between the manipulator and the USV as well as external disturbances is developed. (2) A new type of composite trajectory tracking control strategy based on FOTSM control is designed and applied for the first time to the SBMS. (3) It is proved mathematically that the proposed control strategy can guarantee stability of the closed-loop system while achieving finite-time convergence of tracking errors. Simulation studies demonstrate the effectiveness and efficiency of the proposed control strategy.