The　rapid　development　of　aerospace　technology　has　continuously　promoted　the　demand　for　lightweight　and　systematic　design　of　twisting　structures,　where　advanced　composites　have　drawn　great　expectations.　A　double　helical　structure　has　been　developed　to　introduce　large　axial　twistable　capability,　where　thin-walled　cured　composite　strips　with　a　longitudinal　curvature　were　prestressed　or　flattened　to　be　employed　as　shape-changing　units,　and　then　assembled　by　using　rigid　spokes,　pins,　or　webs;　however,　its　twisting　performance　would　be　susceptible　to　thermal　effects,　and　affected　by　the　curvature　variations　induced　by　flattening　and　assembling　of　the　precured　curved　strips.　Here,　we　proposed　a　novel　double　helical　structural　design,　where　thin-walled　curved　tapes　with　transverse　curvature　were　applied　as　the　shape-changing　units　without　prestressing.　The　double　helical　structures　were　produced　and　investigated　with　isotropic　transverse　curved　tapes,　orthotropic　flat　strips,　as　well　as　orthotropic　transverse　curved　tapes,　in　order　to　reveal　its　geometric　curvature　effects-induced　twisting　mechanics.　An　inextensible　shell　model　was　formulated　to　analyse　the　shape-changing　process,　and　expose　the　regulating　mechanisms　on　structural　stability.　Experiments　and　finite　element　analysis　were　carried　out　to　investigate　the　material　and　geometric　curvature　dependencies.　It　is　found　that　the　material　orthotropy　contributes　to　the　bistability　of　the　helical　structure;　geometric　curvature　promotes　the　stiffness　and　shape-changing　stability　of　the　double　helix.　The　twisting　mechanisms　were　then　concluded　in　detail.　These　findings　are　expected　to　facilitate　torsional　structural　design　and　application　of　deployable　composite　structures　for　aerospace　engineering.