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.