The　coupled　adjoint　equation　of　laminar-turbulent　transition　considering　the　suction　control　effect　is　derived　for　the　aerodynamic　design　of　Hybrid　Laminar　Flow　Control　(HLFC)　airfoils.　The　chain　rule,　automatic　differentiation　algorithm,　and　CK　(Coupled　Krylov)　algorithms　are　used　to　accurately　and　efficiently　solve　the　coupled　adjoint　equations.　Finally,　the　gradient-based　optimization　framework,　based　on　the　discrete　adjoint　equations,　for　HLFC　airfoil　is　constructed.　The　transition　prediction　model　adopts　the　eN　method　based　on　the　Amplification　Factor　Model　(AFM).　The　laminar　flight　test　results　show　that　the　transition　prediction　method　based　on　the　AFM　can　effectively　capture　the　transition　phenomenon　induced　by　T-S　(Tollmien-Schlichting)　waves　instability　under　the　influence　of　suction　control.　The　multi-point　design　of　the　laminar　airfoil　is　carried　out　using　the　gradient-based　optimization　framework,　and　comparison　of　the　results　with　those　of　the　gradient-free　optimization.　The　comparison　of　natural　laminar　flow　design　results　show　that　the　gradient-free　optimization　has　a　deformation　trend　similar　to　the　gradient-free　optimization.　The　results　of　multi-point　design　of　the　hybrid　laminar　flow　airfoil　show　that　the　hybrid　laminar　flow　optimization　has　stronger　drag　reduction　ability　than　the　natural　laminar　flow　optimization.　Compared　with　that　of　the　natural　laminar　airfoil,　the　total　drag　of　the　hybrid　laminar　airfoil　is　reduced　by　6.1%,　5.9%,　33.3%,　9.5%,　respectively.　In　conclusion,　the　gradient-based　optimization　method　based　on　the　discrete　adjoint　equations　can　effectively　improve　the　aerodynamic　performance　of　the　HLFC　airfoil,　thereby　providing　methodological　support　for　the　future　drag　reduction　design　of　HLFC.　©　2022　AAAS　Press　of　Chinese　Society　of　Aeronautics　and　Astronautics.　All　rights　reserved.