In recent years, contrastive learning has become a prominent approach in unsupervised learning. Based on its powerful feature extraction capabilities, contrastive learning can make full use of the value of a large amount of unlabeled high-quality data for model training, thereby improving model quality. However, contrastive learning still faces serious privacy leakage issues when used in downstream tasks. Although recent research attempted to address this issue by incorporating differential privacy into model training, these approaches still suffer from low model utility, especially in the scenarios of extracting accurate feature by contrastive learning. In this paper, we propose DP-CLMI, a novel methodology by integrating differential privacy into the feature output layer of the contrastive learning model which acts as a feature extractor and is then used by untrustworthy parties for downstream tasks, thereby safeguarding the privacy of the training data. Our experimental results demonstrate that this method not only maintains a robust guarantee of differential privacy, but also preserves acceptable levels of classification accuracy. Additionally, the methodology proves to be resilient against various forms of membership inference attacks, especially neural network-based MIA.