This paper presents the characteristics of leakage currents flowing through zinc oxide (ZnO) surge arrester elements under the combined direct-current (DC) and 60 Hz alternating-current (AC) voltages. The current-voltage characteristic curves (I-V curves) of the commercial ZnO surge arrester elements were obtained as a function of the voltage ratio a. At constant peak value of the combined DC and AC voltage, the resistive leakage current of the ZnO blocks was significantly increased as the voltage ratio $alpha$ increased. The I-V curves under the combined DC and AC voltages were placed between the pure DC and AC characteristics, and the cross-over phenomenon in both the I-V curves and R-V curves was observed at the low current region. The ZnO power dissipation for DC voltages was less than that for AC voltage in the pre-breakdown region and reversed at higher voltages.