In　order　to　enhance　the　control　performance　of　the　surface-mounted　permanent　magnet　synchronous　machines　(PMSM)　working　under　the　low　frequency　situations,　this　letter　innovatively　proposes　an　accurate　finite　control　set　(FCS)　model　predictive　current　control　(MPCC)　method.　First,　a　novel　predicting　plant　model　in　the　continuous-time　domain　based　on　the　numerical　solutions　of　the　PMSM　state-space　model　(differential　equations)　is　developed.　Without　using　the　linear　discretization　implementation,　the　influence　of　the　low　control　frequency　can　be　eliminated　completely.　Besides,　a　brand-new　calculation　delay　compensation　method　based　on　delay　time　prediction　and　current　precompensation　is　designed　for　the　proposed　FCS-MPCC　strategy.　Finally,　experiments　are　conducted　on　a　PMSM　test　bench　with　the　control　frequencies　of　2　and　1　kHz　to　comprehensively　verify　the　proposed　algorithms.　©　1986-2012　IEEE.