A　partially　time-varying　coefficient　time　series　panel　data　model　with　fixed　effects　is　considered　to　characterize　the　nonlinearity　and　trending　phenomenon　in　panel　data　model.　To　estimate　the　linear　regression　coefficient　and　the　time-varying　coefficient　function,　two　methods　are　applied　with　the　help　of　profile　least　squares.　The　first　one　is　taking　cross-sectional　average　to　eliminate　the　fixed　effects.　The　second　one　is　local　linear　dummy　variable　approach.　In　each　method　we　derive　consistent　estimates　for　both　the　parametric　component　and　non-parametric　trend　function.　The　asymptotic　distributions　of　the　estimates　are　established　when　T　and　N　tend　to　infinity　simultaneously;　where　N　is　the　cross　section　size,　T　is　the　time　series　length.　The　asymptotic　results　reveal　that　the　parametric　component　(non-parametric　coefficient　function)　estimate　based　on　cross-sectional　average　has　a　rate　of　convergence　T-(1/2)　((Th)(-1/2))　that　is　slower　than　that　based　on　local　linear　dummy　variable　approach,　which　is　(NT)(-1/2)　((NTh)(-1/2)),　where　h　is　the　bandwidth.　Furthermore,　block　bootstrap　method　is　used　to　construct　confidence　interval　for　paiametric,　and　nonparametric　components,　respectively.　At　last,　some　simulation.　studies　are　conducted　to　examine　thefinite　sample　performance　for　the　proposed　methods　and　a　real　data　example　is　analyzed.　(C)　2016　The　Korean　Statistical　Society.　Published　by　Elsevier　B.V.　All　rights　reserved.