This paper establishes a method of supply-chain multi-attribute reverse auction. Presuming the tenderers' preference is open, the paper proposes a non-cooperative multi-attribute bidding game model about public construction projects and analyzes the bidding strategies of tenderers and bidders. Through the simulation of a case in China, we find that: (1) the more committed of the tenderers to construction quality and schedule, the greater benefits, enthusiasm in bidding, and tenderer's surplus; (2) the bidder's benefits have a U-shaped relationship respectively with the bidding quality and the construction period; and (3) the greater the bidder's construction quality and period cost coefficients, the smaller the tenderer's surplus. Such conclusions indicate, the improvement of the bidding rules or procedures can contribute to restricting the behavior of tenderer and bidder, furthermore reducing the corruption possibility of public construction projects.