In order to implement phase discrimination in phase-shift laser range finder with accuracy of submillimeter，according to the principles of FFT and apFFT，performances under the influence of white noise and frequency deviation are analyzed by simulation，and the length of sampling points are considered. Results indicate that FFT achieves better performance than apFFT using the same length of sampling points when frequency deviation is small. The standard error of distance measurement using FFT is 0.76mm with 10kHz measuring rate，35dB SNR，0.02 normalized frequency deviation and 50MHz modulation frequency. The FFT is suitable for phase discrimination in high speed and high accuracy phase-shift laser range finder.