Compared with the traditional memristor, it's more significant to research the multivalued memristor in improving the stability and reliability of memristive neural networks. Developing some multivalued memristor emulators is highly attractive since the fabrication and integration of the memristor are not mature at present. This work presents a behavioral‐level model of a general multivalued memristor FPGA that exhibits continuous or discrete behavior, similar to electrochemical metallization memories. The proposed solution has been successfully synthesized and verified on a Xilinx ZYNQ‐7000 FPGA XQ7Z020 with less than 1% hardware utilization. Additionally, to test the synaptic function of the memristor model in artificial neural networks, this paper constructs a quantized artificial neural network based on eight‐valued memristors in FPGA. In the training of the neural network, the pixel values of the images and the network weights are quantized and then mapped to the input voltage and conductance respectively of the memristor during the forward propagation. The experimental results show that the memristive network circuit achieves 92.8% recognition accuracy for 10,000 MNIST images.