The　estimation　of　underlying　hemodynamic　states　from　the　fMRI　data　can　provide　an　objective　representation　of　the　brain　activity　at　the　neuronal　level,　which　can　contribute　to　the　understanding　of　the　brain　operation　mechanism　and　the　development　of　the　brain　cognition　research.　So　far,　many　methods　have　been　proposed　for　estimating　hemodynamic　states　from　the　fMRI　data.　However,　most　of　these　methods　are　limited　to　the　further　consideration　of　the　temporal　characteristic　in　the　hemodynamic　model.　In　addition,　they　require　the　prior　knowledge　on　hemodynamic　model　parameter　values,　which　are　not　measurable　in　the　actual　situation.　Therefore,　this　paper　presents　a　new　approach　based　on　recurrent　neural　network　(RNN)　to　carry　out　the　estimation　of　hemodynamic　states,　which　employs　RNN　to　extract　the　temporal　features　inherent　in　fMRI　time　series.　Firstly,　the　inversion　process　has　been　constructed　by　the　inversions　of　nonlinear　functions　in　the　hemodynamic　model,　which　map　the　BOLD　signal　to　hemodynamic　states.　Then,　a　novel　neural　network　architecture　called　stacked　recurrent　neural　network　(SRNN)　is　used　for　estimating　hemodynamic　states　with　BOLD　signals　by　approximating　the　mapping　relations.　Finally,　the　experimental　results　on　the　simulated　data　have　shown　that　the　new　approach　can　not　only　capture　the　temporal　characteristic　in　the　fMRI　data,　but　also　can　model　the　nonlinear　relationship　between　hemodynamic　states　dynamically.　Copyright　©　2020　Acta　Automatica　Sinica.　All　rights　reserved.