This　paper　proposes　a　new　iterative　compensation　methodology　of　geometric　errors　to　improve　the　machining　accuracy　of　a　non-orthogonal　five-axis　machine　tool　(NOFAMT).　Firstly,　based　on　homogeneous　transform　matrix　(HTM)　and　multi-body　system　(MBS)　theory,　the　relative　motion　constraint　equations　(TRMCEs)　of　the　tool　tip　position　and　tool　orientation　vector　related　to　a　NOFAMT　with　a　nutating　rotary　B　axis　are　established.　Then,　by　utilizing　TRMCEs,　the　mapping　relationships　between　tool　path　and　the　numerical　control　(NC)　command　without　and　with　considering　the　geometric　errors　are　constructed　respectively.　In　order　to　truly　reproduce　tool　motion　trajectory　of　the　machine　tool　driven　by　the　given　NC　command,　the　mapping　relationship　between　the　NC　command　and　tool　cutting　trajectory　is　also　established.　Meanwhile,　procedures　of　iterative　compensation　are　described　by　using　the　aforementioned　mapping　relationships　without　the　traditional　inverse　calculation,　and　the　actual　NC　code　is　generated　in　self-developed　compensation　software.　It　is　not　difficult　to　find　that　the　new　approach　takes　the　difference　between　tool　path　and　tool　cutting　trajectory　as　the　control　objective　and　can　directly　obtain　the　actual　NC　code　controlling　the　machine　tool　to　achieve　the　desired　machining　accuracy.　Finally,　a　cutting　test　is　carried　out　on　the　DMU60P　NOFAMT.　Experimental　results　show　the　developed　iterative　compensation　methodology　is　precise　and　effective　for　NOFAMTs.　Therefore,　compared　with　the　existing　methods,　the　new　method　is　more　direct　and　accurate.　And　its　basic　idea　can　be　applied　to　other　type　of　machine　tools.