A method of growing a group III-V compound semiconductor epitaxial layer on a substrate by use of atomic layer epitaxy grows an aluminum layer on one of {100}, (111)B, ( 111)B, (111)B, and (111)B planes of the substrate by supplying a quantity of aluminum amounting to at least two times a surface density in a group III-V compound semiconductor epitaxial layer or grows an aluminum layer on one of {110} planes of the substrate by supplying a quantity of aluminum amounting to at least three times the surface density in the group III-V compound semiconductor epitaxial layer, and grows a layer of a group V material on the aluminum layer by supplying a quantity of the group V material amounting to at least two or three times a surface density in the group III-V compound semiconductor epitaxial layer. The layer of the group V material and the aluminum layer constituting the group III-V compound semiconductor epitaxial layer.