In　order　to　conquer　the　computational　complexity　problem　caused　by　multiple　sequence　alignment　in　traditional　distance　methods,　this　paper　presents　a　new　tree-construction　method,　which　uses　a　normalized　edit　distance　matrix　between　pairs　of　sequences　and　the　Neighbor-Joining　algorithm　to　construct　phylogenetic　trees.　Using　sequences　of　Nd5,　Nd4,　Cytb　and　mtDNA　respectively　from　11　vertebrate　species　and　20　mammalian　species,　the　method　can　successfully　generate　consistent　phylogenetic　trees　with　those　which　have　been　examined　by　several　other　approaches.