This　article　proposes　a　tracing　method　to　identify　key　geometric　errors　for　a　computer　numerical　control　machine　tool　by　cutting　an　S-shaped　test　piece.　Adjacent　part　relationships　and　machine　tool　errors　transform　relationships　are　described　by　topology　of　the　machining　center.　Global　sensitivity　analysis　method　based　on　quasi-Monte　Carlo　was　used　to　analyze　machining　errors.　Using　this　method,　key　geometric　errors　with　significant　influence　on　machining　errors　were　obtained.　Compensation　of　the　key　errors　was　used　to　experimentally　improve　machining　errors　for　the　S-shaped　test　piece.　This　method　fundamentally　determines　the　inherent　connection　and　influence　between　geometric　errors　and　machining　errors.　Key　geometric　errors　that　have　great　influence　on　machining　errors　can　be　determined　quickly　with　this　method.　Thus,　the　proposed　tracing　method　could　provide　effective　guidance　for　the　design　and　use　of　machine　tools.