Inthispaper,weusethedeformationmethodandG-equivarianttheorytoprovetheexistenceandmultiplicityofharmonicmapsfromanannulustotheunitsphereinR~3withsymmetricboundaryvalue.Inparticular,wecangetinfinitelymanyhomotopicallydifferentharmonicmapsiftheboundaryvalueisS~1-equivariantandnonconstant.