There are provided a method for epitaxial growth capable of securing stable optical and electrical characteristics by minimizing defects produced in a second epitaxial layer when growing the second epitaxial layer on a first epitaxial layer having defects formed therein, and an epitaxial layer structure using the method. The method includes preparing a first epitaxial layer having a defect formed therein, forming a metal quantum dot on the first epitaxial layer, allowing the metal quantum dot to be moved onto a step of the first epitaxial layer due to a difference of surface energy, converting the metal quantum dot into a metal quantum-dot semiconductor crystal having a lattice constant corresponding to that of the first epitaxial layer, and growing a second epitaxial layer on the first epitaxial layer.