Robust optimization of complex uncertain structures usually involves multiple conflicting and competing structural performance indices. Present approaches for achieving the final design of such an optimization problem always involve the decision-making process, which is a demanding task that requires the rich experience and expert skills of designers. To overcome the difficulty, a novel interval robust equilibrium optimization approach is proposed to find the optimal designs of complex uncertain structures based on the robust equilibrium strategy for multiple conflicting and competing structural performance indices. Specifically, a new concept of closeness and crossing coefficient between interval boundaries (CCCIB) is proposed at first, based on which the tri-dimensional violation vectors of all interval constraints can be calculated and the feasibility of a design vector can be assessed. Then the robust equilibrium among multiple objective and constraint performance indices is assessed, based on the results of which the feasible design vectors can be directly ranked according to the robust equilibrium strategy for all structural performance indices. Subsequently, the algorithm for the robust equilibrium optimization of complex uncertain structures is developed by integrating Kriging technique and nested genetic algorithm. The validity, effectiveness and practicability of the proposed approach are demonstrated by two illustrative examples.