A minimum deviation method is proposed for multi-attribute group decision-making problem with ordinal preference of alternatives given by decision makers and weights of them with respect to each attribute. A nonlinear integer programming model minimizing the weighted deviations between the group's ordinal preferences and all individual ones of the alternatives under each attribute is developed and transformed to an assignment problem to obtain the group's rankings of the alternatives under each attribute. The final integrated rankings of the alternatives in the group's opinion are derived similarly. The proposed method extends the Cook-Seiford social selection function to decision-making with multi-attribute and experts' weights, and can obtain unique ranking result. A supplier selection example is presented to illustrate the method.