Quantization, as an effective model compression technique, often requires training or fine-tuning processes and relies on original data, which imposes burdens on computational resources and time while posing challenges to privacy protection. In recent years, data-free quantization, which does not rely on original data, has attracted increasing attention. However, its performance remains limited when applied to ultra-low precision quantization, and many existing studies rely on synthetic data produced by generative networks, which is computationally intensive. To overcome these limitations, this paper proposes a method called Mixed-Precision Batch Normalization Quantization (MQBN) for the quantization of Convolutional Neural Networks (CNN). It estimates the sensitivity of the convolutional kernels via the statistical information of the Batch Normalization (BN) layers, and then performs mixed-precision quantization within each convolutional layer according to the estimated sensitivity. Extensive experiments on ImageNet demonstrate that the proposed method surpasses recent approaches in terms of accuracy, showcasing its superiority for low-precision quantized models without relying on any training data or fine-tuning.