Abstract: During beam injection in Hefei Light Source(HLS), the amplitude of betatron oscillation varies rapidly, and the frequency varies greatly. It is a typical non-stationary process. Using the traditional method to process the time series signal acquired by the bunch-by-bunch measurement system may result in amplitude distortion and phase deviation. Wavelet analysis provides multi-resolution representations of the bunch signal. Subsequently, the oscillation component and baseline drift component can be separated. The locations on timeline and the linear relationships of the components remain the same as the original signal. Compared with the traditional method, the data processing method based on wavelet analysis is capable of analyzing a non-stationary signal and de-noising a signal without appreciable degradation. It will not bring about conspicuous amplitude distortion and phase deviation, and ensures that the subsequent tracking of the evolution of oscillation amplitude, phase, frequency and mode in the time domain is more reliable. Furthermore, the method has been successfully used to extract the amplitude envelope of betatron oscillation and to calculate growth rate and damping rate. It provides an accurate foundation for machine studies, beam diagnosis and the commissioning of bunch-by-bunch feedback system.