A　theoretical　method　is　proposed　in　this　paper　to　calculate　the　unit　curve　of　gear　integrated　error　(GIE).　The　calculated　GIE　unit　curve　includes　the　quasi-static　transmission　error　(TE)　curves　of　the　approach　stage,　the　involute　stage,　and　the　recession　stage　of　the　ZI　worm　and　helical　gear　transmission.　The　misalignments　between　the　two　axes　of　the　worm　and　gear,　as　well　as　the　modifications　or　errors　of　the　tooth　flanks　of　the　gear,　are　considered　in　the　procedure　of　calculation.　Optimization　algorithm　is　introduced　to　replace　the　solving　of　implicit　differential　equations　of　the　conventional　tooth　contact　analysis　(TCA)　method.　It　is　proved　that　the　proposed　method　is　clearer　and　more　convenient　than　the　conventional　TCA　methods　in　calculating　the　GIE　unit　curve.　The　correctness　and　merits　of　the　proposed　method　are　verified　by　two　experiments.