Aiming at the position stabilization control problem of the offshore gangway tip, the expected joint trajectories of the gangway were calculated by inverse kinematics solution to compensate the disturbances of the gangway tip position caused by the ship motions under the waves, and ensure the gangway tip position unchangeable in the inertial coordinate system. Considering the parameter uncertainties and the generalized disturbance forces of the gangway caused by ship motions under waves in the gangway dynamics model, the extended state observer (ESO) was constructed to estimate the total disturbance composed of the parameter uncertainties and the generalized disturbance forces of the gangway caused by ship motions under waves. Furthermore, a terminal sliding mode trajectory tracking control law based on the ESO was designed to ensure the joint trajectories of the gangway tracking the expected trajectories. Theoretical analysis shows that the state estimation error of the constructed ESO is bounded, and the designed ESO based terminal sliding mode control law converges to zero in finite time for the joint position tracking error of the gangway, thereby ensuring that the end point position of the gangway remains unchanged in the inertial coordinate system. Simulation results verify the effectiveness of the designed control law.