A substrate such as a sapphire substrate or the like is set to a molecular beam epitaxy (MBE) apparatus. Next, the temperature of the substrate is elevated to the temperature which is lower than the temperature at which a predetermined ZnO based oxide semiconductor layer (i.e. function layer) is grown (S1). Then, raw materials containing oxygen radical is irradiated to the substrate to grow a buffer layer made of ZnO based oxide semiconductor (S2). Subsequently, the irradiation of oxygen radical is stopped so as to eliminate the influence of oxygen onto the buffer layer (S3). Then, the temperature of the substrate is elevated to the temperature at which the predetermined ZnO based oxide semiconductor layer is grown (S4). After that, raw materials containing oxygen radical is irradiated so as to sequentially grow a ZnO based oxide semiconductor layer as a function layer (S5). As a result, a ZnO based oxide semiconductor layer with low concentration of residual carrier can be grown, and a semiconductor light emitting device such as light emitting diode and laser diode with high light emitting characteristics can be obtained.