Herein,　a　novel　method,　referred　to　as　conformal　precise-integration　time-domain　(CO-PITD)　method,　which　combines　the　precise-integration　time-domain　(PITD)　method　and　the　conformal　mesh　technique,　is　proposed　to　numerically　calculate　the　evolving　electromagnetic　(EM)　fields　in　the　fine-structured　device　with　moving　part　in　time　domain,　particularly　for　3-D　case.　The　EM　parameters　in　the　computation　cells　partially　occupied　by　moving　medium　are　evaluated　with　the　aid　of　the　conformal　mesh　technique.　For　the　implementation　of　the　PITD　method,　the　discretized　Maxwell　equations　in　those　cells　are　modified　due　to　the　temporal　variation,　caused　by　the　movement,　of　the　EM　parameters.　Furthermore,　the　challenge　from　time-variant　coefficient　matrix　is　overcome　by　constructing　an　effective　piecewise　time-constant　substitute.　Meanwhile,　the　stability　condition　and　the　dispersive　relation　of　the　proposed　method　are　both　theoretically　derived.　The　validity　of　the　CO-PITD　method　is　verified　in　the　context　of　several　numerical　experiments.　In　addition,　the　comparisons　with　the　established　methods　show　that　the　proposed　method　is　of　excellent　efficiency　since　a　much　large　time　step　size　is　permitted　in　it.