To　increase　efficiency　of　solving　problems　of　structural　topology　optimization　by　using　the　ICM　(Independent　Continuous　and　Mapping)　method,　some　functions　are　improved　to　approximate　the　step　function　and　its　inverse　function　in　this　paper.　Firstly,　the　polish　function　and　filter　function　in　ICM　method　are　classified　by　their　properties　of　approximation,　and　the　concepts　of　left　polish　function,　upper　polish　function,　fast　filter　function　and　slow　filter　function　are　presented　respectively.　Then　two　discriminant　theorems,　which　distinguish　two　types　of　polish　functions　and　two　types　of　filter　functions　respectively,　are　derived.　Two　corresponding　theorems,　which　represent　the　corresponding　relationships　between　upper　polish　function　and　fast　filter　function,　left　polish　function　and　slow　filter　function,　are　also　proposed.　Furthermore,　a　use　criterion　and　construction　method　of　the　polish　function　and　filter　function　are　given　in　the　paper.　A　new　structural　topology　optimization　model,　which　approximates　the　original　model　with　higher　precision,　is　formulated　by　using　exponential　type　function　as　left　polish　function　to　approximate　the　step　function.　Above　mentioned　strategies　bring　the　nonlinear　degree　of　optimization　model　higher,　so　it　can　solve　the　optimization　model　with　increased　difficulties.　In　order　to　overcome　the　difficulties,　a　sequential　quadratic　approximate　algorithm　is　proposed　based　on　exact　dual　mapping.　Finally,　an　algorithm　is　formulated　by　taking　weight　minimization　with　displacement　constraints　as　an　example.　Compared　with　the　past　results　when　a　power　function　is　used　as　the　polish　function,　it　indicates　that　our　optimization　model　is　more　rational　and　the　corresponding　algorithm　is　more　efficient.　Moreover,　since　the　accuracy　of　approximating　the　step　function　is　increased　by　taking　a　fast　filter　function　as　the　filter　function,　number　of　iterations　of　optimization　solution　is　greatly　reduced.