We　study　the　concurrence　of　arbitrary-dimensional　multipartite　quantum　states.　Analytical　lower　bounds　of　concurrence　for　tripartite　quantum　states　are　derived　by　projecting　high-dimensional　states　to　2　circle　times　2　circle　times　2　substates.　The　results　are　then　generalized　to　arbitrary　multipartite　quantum　systems.　Furthermore,　the　scheme　enables　us　obtain　lower　bounds　of　concurrence　for　arbitrary　four-partite　quantum　states　by　projecting　high-dimensional　states　to　arbitrary　given　lower　dimensional　substates.　By　detailed　examples　we　show　that　our　results　improve　the　existing　lower　bounds　of　concurrence.