Phononic　crystal　(PnC)　is　a　kind　of　periodic　composite　with　elastic　band-gap　characteristics,　the　distribution　of　elastic　materials　within　a　unit　cell　composing　it　has　significant　effect　on　the　band-gaps.　In　this　paper,　a　topology　optimization　(TOP)　technique　is　utilized　to　obtain　two-dimensional　(2D)　square　lattice　Cu/Epoxy　PnCs　with　maximized　relative　band-gaps　between　multiple　consecutive　bands.　This　optimization　follows　two-stage　design　process　which　adopts　genetic　algorithms　(GAs)　and　plane　wave　expansion　method　(PWE).　The　results　show　that　the　optimal　PnCs　with　different　band-gaps,　which　can　easily　be　obtained　by　the　developed　method,　have　different　material　layout,　and　the　PnCs　with　the　lowest　band-gap　are　simple　lattice　and　have　very　high　application　value.　©,　2015,　Huazhong　University　of　Science　and　Technology.　All　right　reserved.