Geometric　error　is　one　of　the　important　errors　that　affect　the　machining　of　five-axis　machine　tools　and　how　to　identify　th8e　vital　geometric　error　is　effective　for　compensation.　For　this　reason,　the　global　sensitivity　analysis　of　geometric　errors　for　five-axis　machine　tools　is　an　effective　means　to　find　the　vital　geometric　error　items　that　affect　the　machining　accuracy　of　machine　tools.　However,　it　is　difficult　to　deal　with　the　higher　order　items　of　error　parameter　coupling　in　the　global　sensitivity　analysis.　In　this　paper,　a　novel　global　sensitivity　analysis　method　for　vital　geometric　error　based　on　multi-body　theory　and　truncated　Fourier　expansion　is　proposed.　First,　multi-body　system　(MBS)　and　homogeneous　transformation　matric　(HTM)　methods　are　used　to　establish　the　position　error　of　the　machine　tool.　Then,　the　output　value　of　the　error　parameter　is　represented　as　the　amplitude　of　the　truncated　Fourier　series　and　the　global　sensitivity　index　is　represented　by　the　ratio　of　its　amplitude　variance　to　the　total　function　variance　through　normalization　processing.　Moreover,　the　global　sensitivity　analysis　method　is　presented　to　calculate　the　sensitivity　index　of　each　geometric　error　parameter　and　the　vital　geometric　error　parameters　have　been　identified.　Finally,　an　experiment　on　compensating　for　vital　geometric　error　parameters　is　performed　and　the　experimental　results　show　that　the　proposed　method　is　feasible　and　accurate.