We study the photorefractive effect in a thin liquid crystal grating by numerical simulation. The cell consists of homeotropically aligned liquid crystal film sandwiched between photo-conductive electrodes. A constant voltage is applied across the cell. The interference pattern from two impinging laser beams then causes a periodic modulation of the potential at the top and bottom surfaces of the liquid crystal cell. We compare results obtained by simulation with an analytical approach which uses the Geometrical Optics Approximation. The results show good agreement between these two methods.