Based on the similarity between the working mechanism of memristors and the synapses of neural networks, a design scheme of perceptron neural networks based on memristors is proposed in this article. Using memristor based perceptron neurons as the basic unit, a single layer perceptron neural network based on memristors is implemented by adding perceptron neurons in parallel. A multilayer perceptron neural network based on memristors is implemented by serially adding a single layer perceptron neural network. The multiclassification function of the single layer perceptron neural network based on memristors was verified through experiments to determine the quadrant of points in a two-dimensional plane, with a classification accuracy of 96.67%. Through logical XOR operation experiments, the ability of the multilayer perceptron neural network based on memristors to handle linear indivisible problems is verified, and the error is zero. The experimental results of multiclassification and linear indivisibility problems confirm the feasibility of the memristor based perceptron network design scheme.