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This paper develops a finite-time output feedback control scheme for dynamic positioning (DP) system of ships in the presence of unmeasured states of ships, unknown dynamic model parameters and unknown time-varying environment disturbances. A novel finite-time extended state observer (FTESO) is first proposed to simultaneously and precisely estimate the unmeasured states of ships, unknown dynamic model parameters, and unknown time-varying environment disturbances in finite time. Second, based on the outputs of FTESO, the terminal sliding mode (TSM) controller is designed to guarantee that the DP system can track the position and heading at desired values in finite time with precise performance. Then, it is proved that all error signals of the closed-loop DP control system can converge to zero in finite time by utilizing the homogeneous method and the Lyapunov stability theory. Finally, the numerical simulations on a supply ship are carried out to illustrate the effectiveness of the proposed finite-time output feedback control scheme.