Machinery health monitoring is a key step in the implementation of Condition-based Maintenance in industry. In this procedure, a quantitative description of machine health condition is necessary for maintenance decision-making. In this paper, we applied singularity analysis with wavelet for data processing and a new concept, Lipschitz exponent function, was proposed based on wavelet transform. A kurtosis based health index was defined, which can be used for maintenance decision-making. The proposed method was validated with two sets of gearbox vibration data in comparison with three other indexes. The results show that kurtosis based health index demonstrates excellent performance.