In this article, a novel edge computing system is proposed for image recognition via memristor-based blaze block circuit, which includes a memristive convolutional neural network (MCNN) layer, two single-memristive blaze blocks (SMBBs), four double-memristive blaze blocks (DMBBs), a global Avg-pooling (GAP) layer, and a memristive full connected (MFC) layer. SMBBs and DMBBs mainly utilize the depthwise separable convolution neural network (DwCNN) that can be implemented with a much smaller memristor crossbar (MC). In the backward propagation, we use batch normalization (BN) layers to accelerate the convergence. In the forward propagation, this circuit combines DwCNN layers/CNN layers with nonseparate BN layers, which means that the required number of operational amplifiers is cut by half as long as the greatly reduced power consumption. A diode is added after the rectified linear unit (ReLU) layer to limit the output of the circuit below the threshold voltage Vt of the memristor; thus, the circuit is more stable. Experiments show that the proposed memristor-based circuit achieves an accuracy of 84.38% on the CIFAR-10 data set with advantages in computing resources, calculation time, and power consumption. Experiments also show that, when the number of multistate conductance is 28 and the quantization bit of the data is 8, the circuit can achieve its best balance between power consumption and production cost.