We propose a non-paraxial diffraction model of the digital micromirror device (DMD) by combining the conventional Fraunhofer diffraction and a simple method of coordinative mapping. It is equivalent to adding aberrations of diffracted wave fields to the aberration-free Fraunhofer diffraction instead of complex integral calculations, allowing the simulated diffraction patterns to be consistent with the actual experimental counterparts. Moreover, it is verified by the experiments and literature that the diffraction angles, orders, and efficiency can all be well predicted for arbitrary incident angles and wavelengths. Especially for diffracted zenith angles within 50°, the predicted values reveal ∼1% error, and in a broader range, the predicted errors of diffracted azimuth angles are less than 4%. To the best of our knowledge, it is the first model capable of describing the non-paraxial diffraction behavior of the DMD. The proposed model with universality and effectiveness will help users to optimally construct DMD-based optical systems by guiding optical layouts, selection of light sources, and utilization and suppression of diffraction effects.