Failure mode and effects analysis (FMEA) is an important risk analysis tool that has been widely used in diverse areas to manage risk factors. However, how to manage the uncertainty in FMEA assessments is still an open issue. In this paper, a novel FMEA model based on the improved pignistic probability transformation function in Dempster–Shafer evidence theory (DST) and grey relational projection method (GRPM) is proposed to improve the accuracy and reliability in risk analysis with FMEA. The basic probability assignment (BPA) function in DST is used to model the assessments of experts with respect to each risk factor. Dempster’s rule of combination is adopted for fusion of assessment information from different experts. The improved pignistic probability function is proposed and used to transform the fusion result of BPA into probability function for getting more accurate decision-making result in risk analysis with FMEA. GRPM is adopted to determine the risk priority order of all the failure modes to overcome the shortcoming in traditional risk priority number in FMEA. Applications in aircraft turbine rotor blades and steel production process are presented to show the rationality and generality of the proposed method.