In　this　paper,　novel　non-involute　cylindrical　gears　are　designed　based　on　a　curved　path　of　contact.　Firstly,　a　parabolic　curve　is　predesigned　as　the　contact　path　of　novel　gears.　Then,　the　tooth　profiles　of　the　novel　gears　are　calculated　using　differential　geometry　and　spatial　meshing　theory.　Secondly,　the　three-dimensional　tooth　models　of　the　novel　non-involute　gears　are　established　according　to　a　machining　simulation.　Thirdly,　a　simulation　model　(including　misalignment　error　and　longitudinal　modification)　is　established　to　analyze　the　performance　of　the　novel　non-involute　gears.　Finally,　an　example　is　given,　and　the　results　show　that　the　presented　novel　non-involute　gears　have　greater　load-carrying　capacity　compared　with　the　involute　gears.　Moreover,　whether　modified　or　not,　with　or　without　misalignment　error,　the　stresses　of　the　presented　novel　gears　are　lower　than　those　of　involute　gears.