A new grating tiling device with 2×2 gratings is developed to obtain a large aperture grating. For the stability of the device impacted by the HVAC vibration, a dynamic finite element analysis model is established. The random vibration response of the model under the measured power spectral density as stimulus has been carried out by the ANSYS software, and the data has been compared to the experimental data. The results show that the device can meet the stability requirements in the work environment.