The dynamic properties and non-linear control of the pneumatic muscle actuator (PMA) were investigated in this study for use in a specially designed hand rehabilitation device. The phenomenological model of PMA was established in the lower pressure range applicable for hand rehabilitation. The experimental results show that PMA's characteristics can be approximated by piecewise functions. In order to improve the performance and robustness of control for accurate trajectory tracking, a sliding mode control based on non-linear disturbance observer (SMCBNDO) was designed. The simulation and experimental results demonstrated that the model and the sliding mode control achieved the desired performance in tracking a desired trajectory within guaranteed accuracy. The work indicates that the model and the non-linear control proposed in this study can be applied in PMA-driven hand function rehabilitation devices requiring lower pressures.