In order to comprehensively analyze the equipment support level and solve the problem that the weight of evaluation index is too subjective, a method for calculating the index weight of norm grey-correlation degree is proposed. The evaluation index system of equipment support capability and the normal cloud membership degree evaluation model are established to determine the degree of each quantitative evaluation result belonging to the evaluation level. The case study shows that this method can improve the evaluation results which are too subjective and the boundary of the membership function is too hard, so it has good practicability.