Curvature tracking and inverse dynamics adaptive control method are proposed to solve the problem of that the precise trajectory tracking control of underactuated unmanned ship becomes difficult due to the influence of nonholonomic constraint and model imprecision. In the first place， we establish the kinematics and dynamics models on the horizontal plane. Then， the original problem is transformed into a simple tracking control problem by making full use of the motion law under the nonholonomic constraint and introducing the relative curvature of the target curve to construct a dynamical tracking target. After that， the torque controller is designed to realize a given motion task based on sliding mode control and inverse dynamic adaptive control method. Simulation results show that the curvature tracking method can not only make the underactuated unmanned ship follow a given target trajectory accurately， but also lead to high robustness. Since the proposed method essentially tracks the relative curvature of the target trajectory， it can fundamentally solve the problem of trajectory tracking accuracy of underactuated unmanned ship， which provides a new idea for the precise motion control design of general underactuated nonholonomic mechanical structures.