In the method of fabricating a quantum well structure which includes a well layer and a barrier layer, the well layer is grown at a first temperature on a sapphire substrate. The well layer comprises a group III nitride semiconductor which contains indium as a constituent. An intermediate layer is grown on the InGaN well layer while monotonically increasing the sapphire substrate temperature from the first temperature. The group III nitride semiconductor of the intermediate layer has a band gap energy larger than the band gap energy of the InGaN well layer, and a thickness of the intermediate layer is greater than 1 nm and less than 3 nm in thickness. The barrier layer is grown on the intermediate layer at a second temperature higher than the first temperature. The barrier layer comprising a group III nitride semiconductor and the group III nitride semiconductor of the barrier layer has a band gap energy larger than the band gap energy of the well layer.