This　paper　presents　a　novel　topology　optimization　method　to　design　graded　lattice　structures　to　minimize　the　volume　subject　to　displacement　constraints　based　on　the　independent　continuous　mapping　(ICM)　method.　First,　the　effective　elastic　properties　of　graded　unit　cells　are　analyzed　by　the　strain　energy-based　homogenization　method.　A　surrogate　model　using　quartic　polynomial　interpolation　is　built　to　map　the　independent　continuous　topological　variable　to　the　effective　elastic　matrix　of　the　unit　cell　and　set　up　the　relationship　between　the　macroscale　structure　and　microscale　unit　cells.　Second,　a　lightweight　topology　optimization　model　is　established,　which　can　be　transformed　into　an　explicitly　standard　quadratic　programming　problem　by　sensitivity　analysis　and　solved　by　dual　sequential　quadratic　programming.　Third,　several　numerical　examples　demonstrate　that　graded　lattice　structures　have　a　better　lightweight　effect　than　uniform　lattice　structures,　which　validates　the　effectiveness　and　feasibility　of　the　proposed　method.　The　results　show　that　graded　lattice　structures　become　lighter　with　increasing　displacement　constraints.　In　addition,　some　diverse　topological　configurations　are　obtained.　This　method　provides　a　reference　for　the　graded　lattice　structure　design　and　expands　the　application　of　the　ICM　method.