The concept of intuitionistic fuzzy sets is the generalization of the concept of fuzzy sets. The theory of intuitionistic fuzzy sets is well suited to dealing with vagueness. In this paper, multi- attribute decision making using intuitionistic fuzzy sets is investigated. A combined maximum and minimum average weighted Intuitionistic index method is proposed. The linear programming models are constructed to determine the weight vector of attributes and then to rank the alternatives. Feasibility and effectiveness of the proposed method are illustrated using a numerical example.