Aiming at the requirements of low power consumption and light computing power for edge smart devices, this paper uses a new type of integrated storage and computing device-memristor as the basic circuit element, and designs low power consumption and image-specific circuits. The circuit uses a series of multiple memristive convolutional layers and a memristive fully connected network to obtain high recognition accuracy. In order to reduce the imbalance of the row size and column size of the memristive interleaved array required for calculation of the memristive convolutional layer, and at the same time reduce the power consumption of the input voltage direction circuit, the input voltage inverter is placed after the memristive interleaved array. This circuit can reduce the row size of the memristive interleaved array required to complete the memristive convolution network operation from 2M+1 to M+1, and at the same time reduce the number of inverters required for the calculation of a single convolution core to 1, which greatly reduces the volume and power consumption of the memristive convolutional network. Using mathematical approximation, the calculations of the BN layer and the dropout layer are merged into the CNN layer to reduce the number of network layers and reduce the power consumption of the circuit. Experiments on the CIFAR-10 data set show that the circuit can effectively classify images, while having the advantages of fast inference speed (136ns) and low power consumption (the power consumption of a single neuron is less than 3.5uW).