Spiking neural network is considered as the third generation of neural networks, and it has attracted many researchers. Its advantages have been shown in pattern recognition and computer vision. The implementation of the spiking neural network in the hardware is an important method to show its powerful computation ability. This paper begins with the synapse response curve, and then in order to suit for the FPGA implementation the difference equation is used to approach the response curve. In addition, the genetic algorithm is used to optimize the parameters of the circuit. According to the difference equation, the circuit is designed in the Simulink platform. The simulation results are obtained for the outputs of circuit triggered by a square impulse wave. Finally the future work is discussed.