In this paper, the position tracking control problem of pneumatic servo systems is investigated. These systems usually have high nonlinearities and unmeasurable piston velocities. Firstly, by using adding a power integrator technique, a global finite-time state feedback controller is proposed. Secondly, based on homogeneous theory, a nonlinear observer is developed to estimate the piston velocity. Finally, the corresponding output feedback controller is derived, which local finite-time stabilizes the position tracking error system. Compared with the conventional backstepping output feedback control scheme, the developed nonsmooth output feedback control scheme offers a faster convergence rate and a better disturbance rejection property. Numerical simulations illustrate the effectiveness of the proposed control scheme.