The aim of this paper is to investigate the multiple attribute decision making problems to select the bridge construction projects with interval-valued intuitionistic fuzzy information, in which the information about attribute weights is completely known, and the attribute values take the form of interval-valued intuitionistic fuzzy numbers. A modified TOPSIS analysis method is proposed. Then, based on the traditional TOPSIS method, calculation steps for solving interval-valued intuitionistic fuzzy multiple attribute decision-making problems with known weight information are given. Finally, an illustrative example involving a bridge construction project selection is given to verify the developed approach and to demonstrate its practicality and effectiveness.