Aiming at the problem of a poor signal-to-noise ratio in the laser Doppler acceleration measurement system, the digital correlation phase-detection algorithm was proposed for acceleration demodulation. The phase difference between the two interference signals in the laser Doppler acceleration measurement system was calculated by the digital correlation phase discrimination algorithm, and the acceleration of target was calculated from the rate of change of the phase difference, thereby the continuous acceleration measurement of the moving object was realized. The simulation results show that the error of the acceleration measurement is 0.135 m/s² and the resolution is 7.3×10^-3 m/s², when the signal-to-noise ratio is 20 dB. The laser Doppler acceleration measurement system was built to measure the acceleration of the piezoelectric ceramic oscillator, the error of the acceleration measurement is 0.13 m/s². The measurement results show that the algorithm can reduce the interference of random noise and improve the accuracy of acceleration measurement.