Based on cosine-style grating，the interference of diffraction by a double grating is studied theoretically with a wavefront phase-factors method. The patterns of Fraunhofer diffraction are shown by some formulas. Intensities’changing of each order diffraction is deduced as one grating translates along another horizontally and vertically. The intensities’changing figures are also shown by numerical simulation. These formulas form a foundation for experimental applications. One of these obvious applications is to measure the amplitude and the frequency of a harmonic micro-vibrating.