This paper addresses the finite-time path following control problem for an under-actuated stratospheric airship with input saturation, error constraint, and external disturbances. To handle the adverse effect of input saturation, anti-windup compensators are employed and finite-time convergence of the saturated control solution is established. Error constraints of airship position and attitude are handled by incorporating a tan-type barrier Lyapunov function (TBLF) in guidance and attitude control schemes. Backstepping design is presented with the anti-windup compensators, the TBLF, and nonlinear disturbance observers which estimate the external disturbances. Stability analysis shows that the tracking errors of the airship position converge into a small set around zero within finite-time, the constrained requirements on the airship position and attitude are not violated during operation, and all closed-loop signals are guaranteed to be uniformly ultimately bounded. Compared with the conventional control scheme, simulation results illustrate that the proposed finite-time controller offers a faster convergence rate and a higher path following accuracy for the stratospheric airship.