We have fabricated GaN quantum dots (QDs) in AlN confined layer structures by molecular beam epitaxy. The size distribution and density of the QDs have been estimated from an atomic force microscopy study. Very high quantum efficiency of photoluminescence (PL) has been obtained in some samples with QDs. Compared to the GaN bulk samples, it increased by orders of magnitude. In some samples the quantum size effect dominated, resulting in the blue-shift of the QD related PL peak, whereas in the samples with larger dots a red-shift up to 0.8 eV has been observed, which is related to strong polarization effects. We have observed a blue-shift of the PL peak with excitation intensity in the samples with large dots due to screening effect. The temperature-induced quenching of PL occurs at higher temperatures compared to bulk GaN due to the confinement of nonequilibrium carriers in the QDs. An excited state has been observed in some samples.