We present the design steps for 3D polarization-independent Fabry-Perot cavity. Inclusion of isolated dielectric rods into the limited number of holes at around the central region enables the generation of cavity that sustains both transverse electric and transverse magnetic modes. Localization of light is obtained at the same frequency for both polarizations with moderately high quality factors. Polarization-independent nanobeam cavity is expected to be a platform for studying strong light matter interaction at the wavelength scales.