Abstract: Distributed clustering based on LDP mainly uses K-means clustering algorithms, which faces challenges in adapting to non-convex distributed data and suffers from a significant loss of clustering accuracy due to the proportionality of privacy budget division and dimensionality, leading to the introduction of a large amount of noise. To address these issues, we propose a Gaussian mixture model (GMM) clustering method based on local differential privacy. We designed a parameter pre-selection model that satisfied LDP, which explored the data distribution through a grid structure and determined the initial parameters based on dense distributions. We designed a data coding mechanism based on the Haar wavelet transform to reduce the privacy budget division and noise injection amount through lossless dimensionality reduction. A feedback loop model was constructed between the server and users to optimize GMM parameters and clustering modes iteratively. We proposed a sub-cluster merging mechanism based on model overlap to optimize clustering results. Theoretical analysis and experimental results demonstrate that the proposed method can effectively balance clustering accuracy while satisfying LDP.