The wavelet ridge can effectively extract the modulation features of the transient signal. However, the demodulation effect is greatly influenced by wavelet parameters. Local characteristic-scale decomposition (LCD) is a new time-frequency analysis method. By combining LCD de-noising and a genetic algorithm with wavelet ridge demodulation, a gear incipient fault diagnosis method using the LCD de-noising approach and adaptive wavelet ridge demodulation is proposed to extract transient information from the original signal with a low signal to noise ratio. Furthermore, te proposed method is applied to gear crack fault diagnosis. Firstly, a multi-component AM-FM is adaptively decomposed into a series of intrinsic scale components (ISC). At the same time, the special intrinsic scale component that contains a bundant feature information is selected to realize denoising. Secondly, the genetic algorithm is used to optimize wavelet parameters by wavelet energy entropy, thus attaining an adaptive wavelet. Lastly, the adaptive wavelet ridge demodulation method is used to extract instantaneous amplitude and instantaneous frequency. Experimental data analysis results show that the proposed method can be applied to gear crack fault diagnosis.