4D-CBCT　reconstruction　technique　could　provide　a　sequence　of　phase-resolved　images　to　alleviate　motion　blurring　artifacts　as　a　result　of　respiratory　movement　during　CT　scanning.　However,　4D-CBCT　images　are　degraded　by　streaking　artifacts　due　to　the　under-sampled　projection　used　for　the　reconstruction　of　each　phase.　Based　on　the　high　correlation　of　these　4D-CBCT　images,　estimating　the　deformation　vector　fields　(DVF)　among　them　via　a　deformable　registration　algorithm　is　one　of　the　possible　solutions　to　improve　the　image　quality.　Often,　the　intensity-based　similarity　metric　is　utilized　in　the　optimization　problem　by　minimizing　the　squared　sum　of　intensity　differences　(SSD)　of　the　reference　image　and　the　target　image.　However,　this　metric　is　not　suitable　for　the　4D-CBCT　registration　case,　because　the　quality　of　both　the　reference　image　and　the　target　image　are　not　always　guaranteed.　As　a　result,　the　registration　accuracy　of　the　conventional　SSD　metric　still　has　room　to　improve.　In　our　method,　by　considering　the　characteristic　of　the　phase-depended　images,　we　design　a　novel　similarity　metric:　1)　A　prior　image　reconstructed　by　the　whole　projection　set　is　regarded　as　the　reference　image;　2)　Instead　of　an　intensity-based　similarity　metric　alone,　we　proposed　a　free-form　based　optimization　function　associating　the　gradient　information　in　spatial　domain　with　the　projection-based　constraint.　To　validate　the　performance　of　the　proposed　method,　we　carried　out　a　phantom　data　and　a　patient　data　to　compare　with　the　classical　Demons　algorithm.　To　be　specific,　the　quality　of　the　registered　image　was　improved　to　a　great　extent,　especially　in　regions　of　interest　of　moving　tissues.　Quantitative　evaluations　were　shown　in　terms　of　the　rooted　mean　square　error　(RMSE)　by　our　method　when　compared　with　existing　Demons　method.　©　2020　SPIE.