This paper presents a novel distributed double-consensus algorithm to solve the optimal energy management problem for multiple energy hubs interconnected with each other. The objective is achieved by establishing two interactive and paralleled consensus procedures modified by their corresponding feedback terms. Meanwhile, a novel projection operation method is proposed to map the infeasible values into the feasible operating region. The proposed algorithm can effectively handle the coupled variables problem existing in the objective function and constraint limits. Moreover, the optimality and convergence analysis are performed strictly under strong connectivity conditions only. Simulations performed on standard test cases are provided to illustrate the effectiveness of the proposed distributed algorithm.