A polarization-independent, high-index contrast grating (HCG) with a single layer of cross stripes allowing simple fabrication is proposed. Since the cross stripes structure can be suspended in air by selectively wet-etching the layer below, all the layers can be grown at once when implemented for vertical-cavity surface-emitting lasers. We optimized the structure to have a broad and high reflectivity band centered at around 1 μm using a finite difference time domain method, and obtained an 80 nm high reflectivity band centered at 0.97 μm in which the reflectivity exceeded 99.5%. We also investigated the fabrication tolerances of the structure and found that, assuming careful optimizations of electron beam lithography for the precise grating width and dry-etching for the vertical sidewall, the suggested polarization-independent HCG can be fabricated using standard technologies.