The aim of this paper is to investigate the multiple attribute decision making problems with interval-valued intuitionistic fuzzy information, in which the information about experts weights and attribute weights are completely unknown, and the attribute values take the form of interval-valued intuitionistic fuzzy number. We developed a multiple attribute decision making method by computing the scores of all alternatives in interval-valued intuitionistic fuzzy setting, by which the attribute weights and experts weights can be determined. A new score function is constructed to evaluate the alternatives. Finally, an example is presented to highlight the procedure of the proposed algorithm.