Continuous　fiber-reinforced　polymers　(CFRPs)　have　been　widely　applied　in　aerospace　and　other　fields　due　to　their　excellent　mechanical　properties,　which　highly　depends　on　the　material　distribution　and　fiber　orientations.　The　designability　of　CFRP　structures　and　fiber　distributions　provides　an　opportunity　for　achieving　better　physical　properties　through　optimization.　However,　local　optima　and　the　dependence　of　initial　fiber　angle　variables　make　the　concurrent　optimization　of　fiber　orientation　and　topology　a　challenging　problem.　In　this　paper,　the　principal　stress　orientation　interpolated　continuous　fiber　angle　optimization　(PSO-CFAO)　method　combined　with　the　independent　continuous　mapping　(ICM)　method　is　proposed　to　realize　the　design　of　CFRP　structures　with　a　clear　macroscopic　topology　and　microscopic　fiber　distribution.　A　sigmoid　function　is　applied　to　interpolate　the　fiber　angle　variables　by　the　principal　stress　orientation.　The　fiber　angle　variables　are　modified　and　a　continuous　fiber　design　is　obtained　during　the　iteration　process,　which　reduces　the　possibility　of　a　local　optimum.　Several　examples　are　provided　to　prove　the　effectiveness　and　stability　of　the　proposed　method,　and　the　expected　results　are　acquired　for　different　initial　fiber　angles,　material　parameters　and　mesh　densities.　The　proposed　method　provides　guidance　for　the　design　of　CFRP　structures　and　the　planning　of　fiber　laying　paths.　©　2023　Elsevier　Ltd