The present disclosure, belonging to the field of display technology, provides a grating assembly, a light source apparatus and a driving method thereof, which can solve a problem that an existing light source cannot provide light with a controllable direction. The grating assembly of the present disclosure comprises: a diffraction grating divided into a plurality of sub-pixels, each sub-pixel being divided into a plurality of regions, the diffraction grating being configured to change light transmitted through each region into parallel light and cause light transmitted through different regions of a same sub-pixel to have different directions; and a selector divided into a plurality of sub-pixels corresponding to sub-pixels of the diffraction grating, each sub-pixel being divided into a plurality of regions corresponding to the regions of the sub-pixel of the diffraction grating, the selector being configured to control whether each region thereof transmits light or not.