The　topology　optimization　with　frequency　constraints　is　mainly　focused　on　the　continuum　structures　currently,　however,　the　researches　on　topology　optimization　for　frame　structures　with　frequency　constraints　are　relatively　less.　To　obtain　the　optimal　frame　structures　with　frequency　constraint,　it　is　necessary　to　conduct　research　on　the　topology　optimization　for　frame　structures　with　frequency　constraint.　Based　on　ICM　(independent,　continuous　and　mapping)　method,　the　zero-one　type　discrete　topology　variables　are　transformed　into　the　continuous　topology　variables　between　zero　and　one.　A　continuous　topology　optimization　model　is　established　to　minimize　the　weight　with　frequency　constraint.　Based　on　the　behavior　research　of　frequency　constraints　for　frame　structures,　two　different　power　functions　were　introduced　as　the　filter　function　to　explicit　the　frequency　constraints　approximately.　The　object　and　constraints　were　both　expressed　as　the　first-order　Taylor　expansions　of　topology　variables　to　establish　the　linear　programming　model.　The　movable　limits　were　adopted　to　control　the　step　size　of　topology　variables　in　order　to　avoid　the　iterative　oscillation　and　ensure　the　optimization　accuracy.　The　numerical　examples　show　that　the　linear　programming　model　based　on　ICM　method　can　efficiently　solve　the　topology　optimization　problem　with　base　frequency　constraint　for　frame　structures.　©,　2015,　Beijing　University　of　Technology.　All　right　reserved.