Photonic chips have great potential for neural network computing due to their fast speed, low power consumption, and parallelism. We propose a quantized neural network modeling method based on microring resonators (MRR). We analyze the optical properties of the MRRs and utilize lasers with different wavelengths as inputs of the neural network. The quantization aware method is adopted to train the neural network, and the stochastic search method is utilized to determine hyperparameters of the network. We transform the network parameters and hyperparameters into MRR parameters to simulate neural network matrix multiplication operations. Finally, we used the Mixed National Institute of Standards and Technology database for testing the proposed model. For 4-, 5-, and 6-bit quantization of weight parameters, we obtain classification accuracies of 94.23%, 94.73%, and 96.11%, respectively. Thus our study demonstrates the feasibility of building a neural network inference system using a microring structure and provides a theoretical support for applying MRRs in neural networks.