Abstract: The effect of exponentially decaying threshold on a Gaussian white-noise driven integrate -and-fire(IF) neuron is studied,especially on the mean and standard variance of the interspike interval.The results indicate that for slow threshold decay,the IF model shows a minimum in the variate coefficient of interspike interval whenever the firing rate of the neuron matches the decay rate of the threshold.The effect on the firing rate can be seen by change the noise intensity or the input current.The errors are analyzed which are caused by resetting the membrane potential after firing.The application to image edge detection shows the good effect of the IF network.