In this letter, a multi-layer memristive neural network in which memristors serve as memory factor and impact factor is built for the binary images learning.Unlike the traditional artificial neural networks, the memristive neural network is trained with noise samples for the introduction of image overlay.A similarity recognition based on the impact factor for binary images is employed to exhibit the function of the memristive neural network.The Simulinks and the experiments shows that the proposed memristive neural network has quick learning speed and high noise tolerance.