The　topological　optimization　model　for　the　continuum　structure　is　constructed,　which　has　the　minimized　weight　objective　and　frequency　constraints.　The　model　is　transferred　into　a　dual　optimization　model;　and　sequential　quadratic　programming　is　adopted　to　solve　it.　Some　numerical　problems,　such　as　the　checkerboard　patterns,　the　mesh　dependence,　the　local　modal　and　modal　switch　problems,　are　eliminated.　The　topology　optimization　model　with　the　minimized　weight　objective　is　unified　with　the　models　of　size　and　shape　optimization.　It　also　has　advantages　in　dealing　with　multi-frequency　constraints　and　solving　the　modal　switch　difficulties.