The discrete wavelet transform based on the orthogonal wavelet bases has the disadvantage of shift-variant. In this paper, using the compactly supported dyadic orthogonal real-valued wavelet bases to construct the compactly supported dyadic orthogonal linear phase complex wavelet (LCW) bases in terms of alternately lifting scheme. Linear phase complex wavelet can separate the envelope of the flicker signal. The core of the method is a pair of Hilbert transform including the flicker signal in wavelet field is come into being, i.e. a pair of quadrature components with the same amplitude and the same frequency can be used to realize the demodulation of an amplitude modulated voltage flicker signal. Simulation experiments show the method proposed has the characteristic of shift-invariant comparing with the traditional discrete wavelet transform, result of separating envelope of the flicker signal is independent of initial time recording signal.