Conventional fuzzy inference algorithms cannot effectively solve the inverse heat transfer problems with complex or unknown heat transfer laws. In this paper, a feedback-fuzzy inference global method is proposed. Based on the basic process of fuzzy inference, variable universe method, feedback thought and simulated annealing algorithm are combined. The dependence of fuzzy rules on heat transfer law is reduced by feedback unit, and the local optimum is prevented by simulated annealing unit. This method was employed to solve the geometric structural design problem of air-cooled radiator fins. The results were compared with those of conventional fuzzy inference and simulated annealing algorithm. And the results of feedback-fuzzy inference global method under different initial values and input errors were verified and compared. The results showed that the proposed method could solve the inverse heat transfer problem with complicated or unknown heat transfer law, and the results were not affected by initial values. The method demonstrates robustness and resistance to ill-posed problems, which can provide a reference for inverse problems, structural design and optimization.