High-quality polycrystalline GaN layers are grown on quartz (silica) glass substrates by gas source molecular beam epitaxy (MBE). The relationship between growth conditions and photoluminescence (PL) properties is systematically studied by changing the growth temperature and Ga/N-2 flux ratio. It is found that the growth temperature is an important factor for the growth of high-quality polycrystalline GaN, which shows very narrow and strong PL emission without yellow luminescence. The PL peak energy dependence on strain between GaN and substrate is observed. The origin of the PL emission is also studied.