Abstract: As an effective risk evaluation method, the Failure mode and effect analysis (FMEA) has been widely adopted to assist in controlling risk and enhancing the reliability of the system in a variety of workplaces. Nevertheless, the current risk prioritization approach for FMEA is insufficient to fully handle the deviation among risk evaluation information from experts with different professional backgrounds in the existing literature. With the intention of remedying this gap, this study put forward a novel risk evaluation and prioritization method for FMEA based on grey theory. Firstly, in order to cope with the deviation in risk evaluation information, which is caused by extreme information from group decision-making, the interval grey number is used as language variables for risk evaluation by experts with different professional backgrounds. Secondly, consider the correlation among risk factors, the important weight of these risk factors is determined by grey relational analysis and entropy measurement method. Thirdly, the grey target decision approach is adopted to decide the priority of these failure modes. Finally, an instance of an aircraft landing system is used to verify the viability and application of this proposed method.