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This work targets the commonly used FPGA (field-programmable gate array) devices as the hardware platform for DNN edge computing. We focus on DNN quantization as the main model compression technique. The novelty of this work is: We use a quantization method that supports multiple precisions along the intra-layer dimension, while the existing quantization methods apply multi-precision quantization along the inter-layer dimension. The intra-layer multi-precision method can uniform the hardware configurations for different layers to reduce computation overhead and at the same time preserve the model accuracy as the inter-layer approach. Our proposed ILMPQ DNN quantization framework achieves 70.73% Top1 accuracy in ResNet-18 on the ImageNet dataset. We also validate the proposed MSP framework on two FPGA devices i.e., Xilinx XC7Z020 and XC7Z045. We achieve 3.65× speedup in end-to-end inference time on the ImageNet, comparing with the fixed-point quantization method.