Translocation　has　been　long　learned　as　a　basic　operation　to　rearrange　the　structure　of　a　genome.　Translocation　sorting　asks　to　find　a　shortest　sequence　of　translocations　that　transforms　one　genome　into　another,　which　has　attracted　attention　of　many　scientists　in　algorithm　design.　Signed　translocation　sorting　can　be　solved　in　polynomial　time.　Unsigned　translocation　sorting　turns　out　to　be　NP-Hard　and　Max-SNP-Hard.　The　best　known　approximation　algorithm　by　now　for　unsigned　translocation　sorting　can　achieve　a　performance　ratio　1.408.　In　this　paper,　we　propose　a　new　approximation　algorithm　for　unsigned　translocation　sorting　which　can　achieve　a　asymptotic　performance　ratio　1.375.　(C)　2020　Elsevier　Inc.　All　rights　reserved.