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This paper reports that the GaN thin films with Ga-polarity and high quality were grown by radio-frequency molecular beam epitaxy on sapphire (0001) substrate with a double A1N buffer layer. The buffer layer consists of a high-temperature (HT) AlN layer and a low-temperature (LT) AlN layer grown at 800℃ and 600℃, respectively. It is demonstrated that the HT-AlN layer can result in the growth of GaN epilayer in Ga-polarity and the LT-AlN layer is helpful for the improvement of the epilayer quality. It is observed that the carrier mobility of the GaN epilayer increases from 458 to 858cm2/V.s at room temperature when the thickness of LT-AlN layer varies from 0 to 20nm. The full width at half maximum of x-ray rocking curves also demonstrates a substantial improvement in the quality of GaN epilayers by the utilization of LT-AlN layer.