With the continuous development of neural networks, the hardware requirements are getting higher and higher, and the emergence of memristors is expected to optimize this challenge. In this paper, by studying the inter-mapping relationship between memristor arrays and neural networks, a memristor-based convolutional neural network circuit module is designed, a binarization method is used to quantize the neural network, an acceleration module is constructed based on multiple computational arrays, and an additive tree is used to accumulate the intermediate results of the output values of multiple computational units. Simulation experiments were conducted with the help of simulation software to compare and analyze the memristor-based CNN with other neural networks. Compared with LSTM, RNN, and ELM, the accuracy of the memristor-based CNN is 4.17%, 7.48%, and 2.01% higher compared to other neural networks, respectively. In the performance analysis, the recognition rate of the memristor CNN is almost unaffected by the programming error and still achieves a recognition rate close to 98% in the best case. This study provides a new idea for implementing and applying convolutional neural networks in memristor arrays, which is expected to promote the further development of memristor neuromorphic computing.