A software phase-locked amplifier demodulation method is proposed in order to demodulate the second harmonic (2f) signal of quasi-continuous laser wavelength modulation spectroscopy (WMS) properly, based on the analysis of its signal characteristics. By judging the effectiveness of the measurement data, filter, phase-sensitive detection, digital filtering and other processing, the method can achieve the sensitive detection of quasi-continuous signal. The method was verified by using carbon dioxide detection experiments. The WMS-2f signal obtained by the software phase-locked amplifier and the high-performance phase-locked amplifier (SR844) were compared simultaneously. The results show that the Allan variance of WMS-2f signal demodulated by the software phase-locked amplifier is one order of magnitude smaller than that demodulated by SR844, corresponding two order of magnitude lower of detection limit. And it is able to solve the unlocked problem caused by the small duty cycle of quasi-continuous modulation signal, with a small signal waveform distortion.