The improved failure mode and effects analysis (FMEA) based on the fuzzy set theory and gray relational theory was proposed for the solution to effective quantization questions of risk analysis in bidding strategy. First of all, combining with the fuzzy set theory, the fuzzy linguistic terminology set of the failure mode and corresponding fuzzy numbers were established, and the different failure modes were evaluated by the FMEA team. Next, the relevance ratio of different failure modes was calculated using the gray relation theory and the risk order of failure modes was confirmed by sorting. Risk analysis cases of biding strategy illustrate the usability and effectiveness of the proposed approad.