Integrated energy systems become more and more important to realize the energy complementary property. Microintegrated energy system, served as the terminal integrated energy system, will have the electricity delivered directly to the local customers by energy hubs (EHs). Here, the data and information of the EHs during the operation are confidential and should be kept by each owner. Therefore, this article designs a dual-decomposition-based distributed algorithm to address this problem, where the optimal consensus problem is used for the dual problem to update the multipliers. The primary and dual problems are alternatively solved until the Karush–Kuhn–Tucher condition is satisfied. For the proposed distributed algorithm, the feasibility can be strictly guaranteed during the iteration process. Moreover, theorems and lemmas are proved for the linear convergence rate. The numerical results verify the effectiveness of the proposed algorithm.