Robotic　manipulators　are　widely　used　for　precise　operation　in　the　medical　field.　Vibration　suppression　control　of　robotic　manipulators　has　become　a　key　issue　affecting　work　stability　and　safety.　In　this　paper　an　optimal　trajectory　planning　control　method　to　suppress　the　vibration　of　a　variable-stiffness　flexible　manipulator　considering　the　rigid-flexible　coupling　is　proposed.　Through　analyzing　the　elastic　deformation　of　the　variable-stiffness　flexible　manipulator,　a　distributed　dynamic　physical　model　of　the　flexible　manipulator　is　constructed　based　on　the　Hamilton　theory.　Based　on　the　mathematical　model　of　the　system,　the　design　of　the　vibration　damping　controller　of　the　flexible　manipulator　is　proposed,　and　the　control　system　with　nonlinear　input　is　considered　for　numerical　analysis.　According　to　the　boundary　conditions,　the　vibration　suppression　effect　of　the　conventional　and　the　variable-stiffness　flexible　manipulator　is　compared.　The　motion　trajectory　of　the　variable-stiffness　flexible　manipulator　and　compare　the　vibration　response　from　different　trajectories.　Then,　with　minimum　vibration　displacement,　minimum　energy　consumption　and　minimum　trajectory　tracking　deviation　as　performance　goals,　the　trajectory　planning　of　the　variable-stiffness　flexible　manipulator　movement　is　carried　out　based　on　the　cloud　adaptive　differential　evolution　(CADE)　optimization　algorithm.　The　validity　of　the　proposed　trajectory　planning　method　is　verified　by　numerical　simulation.