In this article, we propose a dual-gate dielectric face tunnel field-effect transistor (DGDFTFET) that can exhibit three different output voltage states. Meanwhile, according to the requirements of the ternary operation in the ternary inverter, four related indicators representing the performance of the DGDFTFET are proposed, and we explain the impact of these indicators on the inverter and confirm that better indicators can be obtained by choosing appropriate design parameters for the device. Then, the ternary inverter implemented with this device can exhibit voltage transfer characteristics (VTCs) with three stable output voltage levels and bigger static noise margins (SNMs). In addition, by comparing the indicators of the DGDFTFET and a face tunnel field-effect transistor (FTFET), as well as the SNM of inverters, it is demonstrated that the performance of the DGDFTFET far surpasses the FTFET.