A solenoid actuator characterized by low price, available small size, and convenience is one of the main components of production equipments requiring compact, high-speed actuators. When the response needs to be under few milli-seconds, sensing the position of the actuator is much harder because of the inherent low inertia. Improvement of the required performance of these actuators can be obtained by the simulation using a mathematical model. In this study, the mathematical model is presented and proved by comparing the responses of the actual solenoid and of the simulation. The position of the actual solenoid was measured by the eddy current sensor. The simulation was executed using SIMULINK$^{(R)}$.