The grating lateral-shear interferometry has a wide range of applications in wavefront sensing. The lateral-shear interferometer based on Ronchi grating can be applied for high-precision wavefront aberration detection of lithography projection lenses, which is one of the critical issues to overcome lithography challenges. The conventional Ronchi shearing interferometer object grating consists of two sets of one-dimensional Ronchi grating lines perpendicular to each other in order to obtain wavefront information in two directions, namely X and Y. During the experiment, one set is moved into the optical path for phase shifting and measurement, then the other set of grating lines is repeatedly operated. To reduce the complexity of experimental operations, this paper proposes a lateral-shear interference system based on double checkerboard gratings. The object grating and image grating are both set as checkerboard grating, and the rotation angle of the checkerboard grating varies according to the optical system's shear rate, allowing each phase shift to obtain wavefront information in X and Y directions. Multiple uniform phase shifts are performed to extract ± 1 order diffraction wavefronts of X and Y directions. The shear wavefront of the optical system to be measured is calculated from the fourwave interference light field, then the original wavefront can be restored by differential Zernike. Through theoretical analysis and simulation, this double checkerboard system can achieve wave aberration measurement with the same accuracy as traditional Ronchi interferometers, improving the real-time performance of projection lenses wave aberration measurement, and providing more possibilities for subsequent structural improvements of Ronchi lateral-shear interferometer.