With　a　view　to　reducing　the　springback　and　twist　of　PEEK　during　the　incremental　forming　process,　the　ultrasonic　vibration　is　introduced　into　polymer　thermal　single-point　incremental　forming　process　(SPIF).　In　this　study,　the　effects　of　temperature　and　ultrasonic　vibration　on　twist　and　springback　of　formed　parts　are　investigated.　Several　modified　tool　trajectories　are　developed,　and　the　influence　of　tool　trajectory　on　twist　and　springback　are　also　studied.　Finally,　the　microstructures　of　PEEK　parts　are　analyzed　by　XRD.　The　results　show　that　the　increase　of　temperature　is　helpful　to　reduce　the　twist　and　springback.　The　ultrasonic　vibration　is　beneficial　to　the　improvement　of　geometric　accuracy,　while　the　side　wall　bulge　aggravates　at　140 　after　the　ultrasonic　vibration　is　applied.　The　optimized　tool　trajectory　can　effectively　eliminate　twist　and　reduce　the　springback　of　PEEK　parts.　The　XRD　result　shows　that　the　ultrasonic　vibration　is　helpful　to　increase　the　molecular　chain　orientation,　improve　crystallinity,　and　refine　crystallite　at　60 　and　100 .　However,　the　opposite　trend　occurs　at　140 　due　to　the　disorientation　effect　of　molecular　chain.　©　2022,　The　Author(s),　under　exclusive　licence　to　Springer-Verlag　London　Ltd.,　part　of　Springer　Nature.