Abstract: For multiobjective optimization the importance degree of design objectives and the fuzzy description of importance degree are presented in this paper. The weight factors for design objectives are chosen on the basis of importance degree defined by the decision makers in fuzzy environment. Based on the fuzzy importance degree and some compromise strategies, an effective multiobjective optimum design approach, combined with the genetic algorithm, is developed to implement the multiobjective optimum design of composite laminates with damage tolerance. It is shown from the illustration examples that this approach can give the most satisfactory design.