The displacement sensor based on the principle of double diffraction grating interference has many advantages, such as the large measurement range, high accuracy and so on. The principle of this sensor is explained and simulated with ZEMAX. At the same time, the light intensity distribution in the interference field is studied based on the angular spectrum theory. The result shows that the trigonometric distribution interference fringes are gained after the laser passing the dual-grating, and the fringes move a cycle when the dual-grating moves one grating distance relatively. The factors which may result in the displacement measurements errors of dual-grating sensors and the effect of these factors on the results are studied. Error expressions of some factors are also presented.