By simulating biological synapses with memristors according to the function and principle of biological visual system and by combining the memory characteristic of memristor with high-efficient processing ability in spiking neural network, a three-layer spiking neural network model for image edge extraction is constructed, in which the image edge information is represented by the variation of the memristor conductance. The edge extraction result obtained with this approach has the characteristics of continuity, smoothness, low false leak detection and edge positioning accuracy. Since the processing mechanism of this neural network conforms to the biological counterpart, it offers a new idea for the bionic implementation of biological visual system.