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The health state of airborne fuel pumps is important for the safety of flight mission, so the fault state feature extraction and diagnosis for the pumps become an important factor. Due to the complexity of mechanical systems, the randomicity of the vibration signal behave on different scales, making it necessary to analyze the vibration signal in a multi-scale way. Multi-scale fuzzy entropy (MFE) is based on fuzzy entropy is defined to measure the complexity of time series in different scale factors. The MFE characteristic parameters are input to support vector machine for fault classification. Genetic algorithm is applied into adaptive selection of the best penalty parameter and kernel function parameter. By analysis experimental data, the results show that the proposed method can differentiate the fault categories of fuel pumps effectively.