Hand-synchronization can be easily realized in the integrated protection relay and RTU for MV and LV line. If the frequencies between bus bar and transmission line are much different， the sampling with the same time interval will bring about errors in the Fourier algorithm. An effective method is presented to modify the errors in the Fourier algorithm when power frequency deviates from 50 Hz. The theoretical analysis and digital simulation indicate that the modified method can enhance precision by little calculations. Therefore it has great practical value in the project application.