Title: A general differentially private learning framework for decentralized data. Abstract: Decentralized consensus learning has been hugely successful, which minimizes a finite sum of expected objective functions over a network of nodes. However, the local communication across neighboring nodes in the network may lead to the leakage of private information. To address this challenge, we propose a general differentially private (DP) learning framework for decentralized data that applies to many non-smooth learning problems. We show that the proposed algorithm retains the performance guarantee in terms of stability, generalization, and finite sample performance. We investigate the impact of local privacy-preserving computation on the global DP guarantee. Further, we extend the discussion by adopting a new class of noise-adding DP mechanisms based on generalized Gaussian distributions to improve the utility-privacy trade-offs. Our numerical results demonstrate the effectiveness of our algorithm and its better performance over the state-of-the-art baseline methods in various decentralized settings.