An improved FMEA method is proposed in order to deal with multi-granularity problem in evaluating failure modes. Firstly, the 2-tuple linguistic representation is applied in evaluating the pre-set sample E to eliminate the effect of multi-granularity and attain the value of the basic linguistic term. Then, the grey relational theory is applied to the calculation of the gray degree to determine the risk priority of the failure modes. The result shows that the risk priority of the failure modes is explicit.