Multi-material　Topology　Optimization　is　a　simulation　technique　based　on　the　principle　of　the　finite　element　method　which　is　able　to　determine　the　optimal　distribution　of　two　or　more　different　materials　in　combination　under　thermal　and　mechanical　loads.　This　paper　develops　a　lightweight　topology　optimization　formulation　of　multi-material　structures　considering　displacement　constraints　based　on　independent,　continuous　and　mapping　(ICM)　method.　Furthermore,　explicit　expression　of　optimised　formulation　is　derived,　approximations　of　displacement　and　weight　are　given　by　the　first　and　second　order　Taylor　expansion.　And　the　optimization　problem　is　solved　by　sequential　quadratic　programming　approach.　The　feasibility　and　effectiveness　of　proposed　method　are　demonstrated　by　numerical　examples.　It　is　found　that　the　best　transfer　path　of　load　is　provided　using　multi-material　topology　optimization.　The　results　show　that　a　clear　topological　structure　is　obtained　and　the　best　transfer　path　of　load　is　provided　after　multi-material　topology　optimization.　In　addition,　under　the　precondition　of　satisfying　the　displacement　constraint　condition,　the　weight　of　the　optimized　structure　based　on　various　materials　is　lighter.　The　weight　of　multi-material　topology　optimization　structure　decreases　with　the　increase　of　displacement　constraint.　And　the　optimal　topological　structure　of　the　multi-material　is　different　with　the　component　materials.　Besides,　the　optimization　model　established　by　using　the　structural　performance　parameters　as　a　constraint　is　more　reliable　and　more　suitable　for　practical　engineering　applications.　©　Published　under　licence　by　IOP　Publishing　Ltd.