Moire fringe phase difference measurement is the key technology of grating displacement measurement, when the two gratings are in relative movement, moire fringe signal frequency is offset because there is an angle error between the two gratings, traditional multi-phase fast Fourier transform (MPFFT) algorithm is used to calculate moire fringe phase value at any time, it will produce measurement errors, resulting in phase difference measurement is not accurate. To reduce the phase measurement error caused by frequency offset, a phase measurement algorithm of correcting MPFFT is proposed, and phase correction model of MPFFT spectrum based on phase difference correction method is deduced. Simulation results show that in the absence of noise, when the angle error is 0.1°, moire fringe maximum signal frequency offset is 4.19 kHz, the phase measurement error of traditional MPFFT is more than 100°, phase measurement error is less than 0.2°and the phase difference measurement error is less than 0.004° after correction in the presence of Gaussian noise and harmonics, the phase difference measurement error is less than 0.2°. When the pitch is 20 μm, the corresponding grating displacement measurement error is less than 0.0111 μm, it provides a reference for the grating nanoscale displacement measurement.