A Group III atomic layer required for fabrication of a semiconductor quantum nanostructure is grown to be properly restricted to a monolayer.A substrate is configured to have a fast-growth surface portion where growth of a Ga atomic layer proceeds at a relatively high rate and a slow-growth surface portion where the growth of the Ga atomic layer proceeds at a relatively low rate. Ga atoms are supplied to the fast-growth surface portion in an amount not less than that which grows one layer of the Group III atoms. Excess Ga atoms on the fast-growth surface portion are allowed to migrate to the slow-growth surface portion by surface migration, thereby growing only one layer of the Ga atoms on the fast-growth surface portion.