In order to obtain accurate positional and velocity control of a pneumatic actuator system, it is essential to understand how the components in the system work and how they are intergrated. In general, the behaviour of most of the systems can be described mathematically. For examples, the pneumatics of the actuator is easy to model with reasonable accuracy because the geometrical characteristics of the cylinder are usually well understood. However, the control components such as valves are generally more complex because no universal mathematical method exists to describe them adequately. In order to reduce the system cost, simple low-cost on-off valves are used. The nonlinearity associated with on-off valve operation gives rise to more uncertainty in the model. This paper addresses this problem by proposing a novel approach to determine the mathematical model of the pneumatic on-off valve accurately from some simple experimental data. Once the model parameters are calculated by this method, the model can be used as part of a model reference adaptive control algorithm which incorporates the on-off valve model to improve the universal controllability of the pneumatic actuator.