Quantization methods for convolutional neural network models can be broadly categorized into post-training quantization (PTQ) and quantization aware training (QAT). While PTQ offers the advantage of requiring only a small portion of the data for quantization, the resulting quantized model may not be as effective as QAT. To address this limitation, this paper proposes a novel quantization function named Attention Round. Unlike traditional quantization function that map 32 bit floating-point value w to nearby quantization levels , Attention Round allows w to be mapped to all possible quantization levels in the entire quantization space, expanding the quantization optimization space . The possibilities of mapping w to different quantization levels are inversely correlated with the distance between w and the quantization levels, regulated by a Gaussian decay function. Furthermore, to tackle the challenge of mixed precision quantization, this paper introduces a lossy coding length measure to assign quantization precision to different layers of the model, eliminating the need for solving a combinatorial optimization problem . Experimental evaluations on various models demonstrate the effectiveness of the proposed method. Notably, for ResNet18 and MobileNetV2 , the PTQ approach achieves comparable quantization performance to QAT while utilizing only 1024 training data and 10 min for the quantization process .