Continuous　fiber-reinforced　polymer　(CFRP)　has　been　paid　more　attention　to　due　to　its　advantages　of　high　strength,　high　stiffness,　and　lightweight.　However,　it　is　challenging　for　topology　optimization　to　achieve　CRRP　structure　design.　A　topology　optimization　(TO)　model　with　minimizing　structural　compliance　under　volume　fraction　constraint　is　established　based　on　the　independent　continuous　mapping　(ICM)　method.　The　continuous　fiber　angle　optimization　(CFAO)　method　solves　the　fiber　orientation.　Meanwhile,　the　local　optimal　solution　problem　caused　by　the　CFAO　method　is　greatly　avoided　by　the　direction　of　principal　stress.　The　effectiveness　of　the　method　is　verified　by　classic　numerical　examples.　This　paper　has　a　significant　reference　for　the　TO　design　of　CFRP　structure.　©　Published　under　licence　by　IOP　Publishing　Ltd.