Failure mode and effects analysis (FMEA) is a widely used technique for designing, identifying and eliminating known and/or potential failures from system, design and process. In the traditional FMEA, for each failure mode, risk factors of Occurrence, Severity and Detection are evaluated and simply multiplied to obtain a risk priority number. Besides, the weights of three risk factors are also ignored. To overcome these shortcomings of traditional FMEA, we propose a novel FMEA approach for obtaining a more rational ranking of failure modes by integrating entropy weighting method with 'Technique for Order Performance by Similarity to Ideal Solution'(TOPSIS). Finally, a case study about purchasing website is provided to demonstrate the feasibility and benefits of the proposed approach. A plugin in our tool-Breeze is developed to support the proposed approach.