We demonstrate a polarization-insensitive grating device based on a liquid crystal (LC) doped with azo-dyes in polymer networks. The polarization-insensitive diffraction is obtained by periodically modulating the optic axis of a homogeneously aligned nematic LC layer. The polymer networks formed in the doped LC medium play a critical role in achieving the optic axis modulation of the LC by a single pump irradiation. The optically induced effect in the dye-doped LC system is permanent, polarization-insensitive, and electrically controllable.