Aiming at the demodulation of vibration measurement signals by sinusoidal phase modulation laser interferometer, this paper proposes a demodulation method that integrates adaptive filtering and normalized PGC-Arctan. Based on the traditional PGC-Arctan algorithm, this method normalizes the quadrature interferometric signal pair by accurately identifying the carrier phase delay and phase modulation depth, thereby reducing the nonlinearity error of phase demodulation, and introducing an adaptive filter based on the minimum mean square algorithm to filter and reduce the noise of the demodulated signal, further improving the signal's SNDR (signal-to-noise distortion ratio) of the signal. The effectiveness of the algorithm is verified by numerical simulation and experimental testing, and the micro-vibrations of solid surfaces excited by sound waves at frequencies of 100Hz-3KHz are detected and demodulated under laboratory conditions. The results show that the method described in this paper can achieve accurate demodulation of the vibration signal, and the SNDR of the demodulated signal after adaptive filtering is increased by an average of 12dB.