In real-world applications where massive datasets are often stored across distributed computing units, traditional centralized semi-supervised learning (SSL) methods face significant challenges. These limitations include potential privacy risks and sensitivity to non-Gaussian noise. To address these issues, this paper proposes a novel distributed SSL approach that enhances privacy protection by processing data locally and eliminating the need for raw data exchange between units. Unlike conventional SSL algorithms rooted in the minimum mean squared error criterion, our method adopts the maximum correntropy criterion, substantially improving predictive accuracy in the presence of non-Gaussian noise frequently encountered in real-world data. Experiments on both synthetic and real-world datasets confirm that the proposed method outperforms existing approaches in terms of both prediction accuracy under non-Gaussian noise and privacy preservation.