Abstract: In the integrated electricity-gas energy system, the power system and the natural gas system belong to different agents and need to be collaborated distributedly. In the distributed collaboration process under the weakly-centralized framework, the algorithm convergence is achieved through direct information interaction between the agents and the coordination center, and the private information of each agent faces serious risk of leakage. To solve this problem, a full privacy-preserving decentralized coordination algorithm is proposed to achieve the full privacy preservation under the “weakly-centralized framework”. The algorithm introduces the theory of multi-party security computation into the distributed collaborative framework and achieves full privacy preservation in a “weakly-centralized framework” by means of homomorphic encryption technology in the form of ciphertexts for electricity-gas collaboration. Meanwhile, this paper proposes an adaptive convexification and feasibility recovery method to solve the nonconvex natural gas system subproblem, which improves the solution speed. Finally, the effectiveness of the proposed algorithm is verified through the analysis of cases.