Induced current by lightning surge increases monotonically with time, while small oscillating components are superposed on it as shown in the previous papers. In this paper, it is shown that a quench occurs when the induced current exceeds the critical current of superconducting cable, even if amplitude of current oscillation is too small to induce quench by ac losses. Firstly a simplified equivalent circuit and basic equations which can describe the quench due to excess current are proposed. Its applicability is confirmed by the fact that obtained analytic results show good agreement with numerically calculated results by full equivalent circuit and basic equations shown in the previous paper. The dependence of peak value of induced current on wave tail duration of lightning surge is estimated for various voltage-level superconducting transformers by taking account of line surge impedance at secondary side and for the number of simultaneous penetration phase. It is shown that the current peak becomes large in case of underground line at the secondary side and a small % impedance. With the aid of the obtained results, methods to evade the quench are discussed in connection to lightning impulse withstand level and the ratio of transportable current of superconducting cable to the rated current.