Private synthetic data is crucial for data sharing and collaboration, as it can be seamlessly integrated into existing algorithms without requiring additional modifications or privacy concerns. Current methods suffer from inefficiencies in handling high-dimensional data with large domain sizes and limited robustness to data noise, which in turn degrades the quality of the resulting synthetic data. To address these issues, we propose PrivGGM, a novel method for differentially private synthesis of tabular data. PrivGGM first captures correlations within the data by using a robust feature clustering method grounded in fuzzy rough sets, and then privately constructs multivariate Gaussian generative models based on the clustering results. Finally, PrivGGM samples from the models to generate synthetic data, which is then iteratively updated based on the Wasserstein distance to boost utility. We experimentally evaluate PrivGGM on multiple real-world datasets and demonstrate that it outperforms existing methods across a variety of settings and tasks.