In order to overcome the difficulty of feature extraction of non-stationary faulty signals in rolling bearing fault diagnosis under strong noise background, a method based on local characteristic-scale decomposition and synchrosqueezing wavelet transform is proposed. Firstly, the measured vibration signals are processed with LCD and decomposes into a series of intrinsic scale component（ISC）. Then a number of ISCs containing valid information components are selected for SWT and processing them by SWT so that we can extract the effective frequency characteristics. The analysis results from rolling bearing signals with out ring, inner ring and rolling body faults which in a strong noise background shows that comparing with LCD and SWT, the approach of synchrosqueezing wavelet transform based on LCD can effectively suppress the noise and extract the effective signal frequency characteristics. It also has a high time-frequency resolution for accurately determining the operation of rolling bearings. While the method can also effectively reconstruct the signal.