Personalized differential privacy (PDP) offers accurate privacy protection by considering individual differences and personalized privacy preferences, making it suitable for various data release scenarios. However, in traditional PDP mechanism, the coarse-grained personalized sampling method often brings excessive randomness, leading to large sampling errors and low data utility. In this paper, we present a novel mechanism termed as the fine-grained personalized differential privacy (FG-PDP) mechanism, which performs approximating and filtering processes on the un-sampled dataset after the personalized sampling phase within the PDP framework. Then the refined mechanism integrates the newly processed dataset with the sampled dataset and performs noise processing. Furthermore, the privacy and utility analysis shows that the proposed mechanism effectively meets privacy requirements and maximizes the use of un-sampled data, thereby reducing sampling errors and boosting data utility. Finally, the simulating experiments are performed on both synthetic and real-world datasets to compare the FG-PDP mechanism with traditional mechanism. The experimental results show that the proposed mechanism provides significantly enhanced query result accuracy under the same privacy budget. In real-world dataset, the maximum error of the proposed mechanism is smaller than the minimum error of the PDP mechanism when evaluated under average function, while simultaneous exhibiting robust performance.