With the demand on increasing data storage capacity and information processing speed in the modern society, more compact and integrated planar optical devices have received widespread attention. As one of the typical liquid crystal (LC) devices to modulate geometric phase, LC polarization gratings have shown great application potential in optical systems due to the advantages such as high diffraction efficiency, large deflection angle, and short response time, etc. However, some of the problems related to electro-optical performances have not yet been overcome in the current manufacturing process of LC polarization gratings, limiting its practical application. The control of diffraction characteristics of LC polarization gratings is subject to certain preconditions. In this work, by optimizing the elastic continuum model used to analyze the LC polarization grating, the influence of LC physical parameters (elastic constant, dielectric constant, etc.) on the critical cell thickness and threshold voltage, under the strong and weak anchoring conditions were investigated, providing the theoretical support for the selection of LC materials with suitable physical parameters for LC polarization gratings toward different applications.