Design method of axial gradient index (AGRIN) lens is researched.Aberration theory of AGRIN is summarized.Its application in optical design software is briefly introduced.At last three laser beam focusing lenses are designed with one of them AGRIN medium meeting diameter 12mm and wavelength 1.06μm.The first is a common spherical singlet,the second is an aspheric singlet and the third is a spherical singlet including AGRIN medium.From design result the third′s image quality is near diffraction limit which is better than the rest.Their minimum RMSs are respectively 191.75μm,17.69μm and 2.42μm.