In this study, inverter logic circuits on a plastic substrate are built with two top-gate FETs in series on a single ZnO nanowire. The voltage transfer characteristics of the ZnO nanowire-based inverter logic circuit exhibit a clear inverting operation. The logic swing, gain and transition width of the inverter logic circuit is about 90 %, 1.03 and 1.2 V, respectively. The result of mechanical bending cycles of the inverter logic circuit on a plastic substrate shows that the stable performance is maintained even after many hundreds of bending cycles.