Patterned sapphire substrates (PSS) were fabricated by a simple wet etching process with $SiO_2$ stripe masks and a mixed solution of $H_2SO_4$ and $H_3PO_4$. GaN layers were epitaxially grown on the PSS under the optimized 2-step growth condition of metalorganic vapor deposition. During the 1st growth step, GaN layers with triangular cross sections were grown on the selected area of the surface of the PSS, and in the 2nd growth step, the GaN layers were laterally grown and coalesced with neighboring GaN layers. The density of threading dislocations on the surface of the coalesced GaN layer was $2{sim}4;{ imes};10^7;cm^{-2}$ over the entire region. The epitaxial structure of near-UV light emitting diode (LED) was grown over the GaN layers on the PSS. The internal quantum efficiency and the extraction efficiency of the LED structure grown on the PSS were remarkably increased when compared to the conventional LED structure grown on the flat sapphire substrate. The reduction in TD density and the decrease in the number of times of total internal reflections of the light flux are mainly attributed due to high level of scattering on the PSS.