An optically switchable, polarization-independent holographic polymer dispersed liquid crystal (H-PDLC) transmission grating is demonstrated by adding azobenzene-LC and chiral molecules into the H-PDLC formulation. The optical switchable mechanism is from the trans-cis photoisomerization of the doped azobenzene-LC, which modulates the refractive index of the LC rich area. The dependence of the diffraction efficiency of the H-DPLC grating without chiral molecules on light polarization suggests that the orientation of LC directors within the droplet is ellipsoidal and uniaxial. However, the addition of chiral molecules into the H-PDLC formulation helps the formation of isotropic and non-uniaxial LC directors within the droplets. The polarization properties of the grating are investigated and analyzed by the coupled and modified coupled wave theory with a model of sinusoidal dielectric modulation. The results show that the addition of chiral molecules changes the LC phase from nematic to chiral-nematic, where the grating efficiency, which is modulated by the photoinduced phase transition, is independent of the polarization of incident light. Our findings may help improve optical systems that utilize non-polarized light.