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Quantization is wildly taken as a model compression technique, which obtains efficient models by converting floating-point weights and activations in the neural network into lower-bit integers. Quantization has been proven to work well on convolutional neural networks and transformer-based models. Despite the decency of these models, recent works have shown that MLP-based models are able to achieve comparable results on various tasks ranging from computer vision, NLP to 3D point cloud, while achieving higher throughput due to the parallelism and network simplicity. However, as we show in the paper, directly applying quantization to MLP-based models will lead to significant accuracy degradation. Based on our analysis, two major issues account for the accuracy gap: 1) the range of activations in MLP-based models can be too large to quantize, and 2) specific components in the MLP-based models are sensitive to quantization. Consequently, we propose to 1) apply LayerNorm to control the quantization range of activations, 2) utilize bounded activation functions, 3) apply percentile quantization on activations, 4) use our improved module named multiple token-mixing MLPs, and 5) apply linear asymmetric quantizer for sensitive operations. Equipped with the abovementioned techniques, our Q-MLP models can achieve 79.68% accuracy on ImageNet with 8-bit uniform quantization (model size 30 MB) and 78.47% with 4-bit quantization (15 MB).