The effect of interference of diffraction by a double grating is worthy to study theoretically and provides possibilities of application. We calculate the pattern of Fraunhofer diffraction by a cosine-style double grating with a wavefront phase-factors method. Some formulas about intensities of each order diffraction are deduced as one grating translates along another. Some experiment results are shown to coincide with the diffraction patterns 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 micro-vibration.