The grey relation analysis is a kind of quantitative analysis method based on factors compared. The information axiom of axiomatic design provides a mean of evaluation by comparing the information content of several alternatives, based on which a new method for multi-attribute decision making is proposed. First, according to decision matrix of all decision making criteria, the ideal alternative composed of the best reference data series among all alternatives is constructed. Then the information content is used to evaluate the relation grade between an individual alternative and the ideal alternative. The fuzzy preferences are utilized to determine the weight of each criterion. The total information content of every alternative is calculated, and arrayed in order, so the optimal alternative can be selected. For requirements of evaluation, the calculation formula of information content is amended. Finally, an example is given to illustrate the effectiveness and feasibility of the proposed method.