This paper investigates the finite-time attitude tracking control problem of a stratospheric airship's motion system, which is subject to internal parameter perturbations and external disturbances, based on the non-singular terminal sliding mode control algorithm. First, based on the nominal mathematical model of the airship's attitude motion, the attitude motion model is linearized by coordinate transformation and state feedback, while achieving the three-channel decoupling of the attitude motion model. Then, non-singular terminal sliding mode controllers are designed for each channel tracking error model, to achieve the finite-time convergence of the system state to the desired state. Finally, the effectiveness and robustness of the proposed method are verified by numerical simulations. The simulation results show that the designed attitude control system can adjust the desired attitude angle with zero steady-state error under the conditions of internal parameter perturbations and external disturbances, and it improves the response speed of the system compared to traditional linear sliding mode control methods.