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Network quantization, one of the most widely studied model compression methods, effectively quantizes a floating-point model to obtain a fixed-point one with negligible accuracy loss. Although great success was achieved in reducing the model size, it may exacerbate the unfairness in model accuracy across different groups of datasets.This paper considers two widely used algorithms: Post-Training Quantization (PTQ) and Quantization-Aware Training (QAT), with an attempt to understand how they cause this critical issue.Theoretical analysis with empirical verifications reveals two responsible factors, as well as how they influence a metric of fairness in depth.A comparison between PTQ and QAT is then made, explaining an observation that QAT behaves even worse than PTQ in fairness, although it often preserves a higher accuracy at lower bit-widths in quantization.Finally, the paper finds out that several simple data augmentation methods can be adopted to alleviate the disparate impacts of quantization, based on a further observation that class imbalance produces distinct values of the aforementioned factors among different attribute classes. We experiment on either imbalanced (UTK-Face and FER2013) or balanced (CIFAR-10 and MNIST) datasets using ResNet and VGG models for empirical evaluation.