<p>In real-world scenarios, mixture models are frequently employed to fit complex data, demonstrating remarkable flexibility and efficacy. This paper introduces an innovative Pufferfish privacy algorithm based on Gaussian priors, specifically designed for Gaussian mixture models. By leveraging a sophisticated masking mechanism, the algorithm effectively safeguards data privacy. We derive the asymptotic expressions for the Kullback–Leibler (KL) divergence and mutual information between the original and noise-added private data, thereby providing a solid theoretical foundation for the privacy guarantees of the algorithm. Furthermore, we conduct a detailed analysis of the algorithm’s computational complexity, ensuring its efficiency in practical applications. This research not only enriches the privacy protection strategies for mixture models but also offers new insights into the secure handling of complex data.</p>