In this work, the electrical properties of monolayer α-GeTe (ML α-GeTe) based on first-principles were studied, in which armchair α-GeTe shows an ohmic current–voltage relationship and zigzag α-GeTe shows an obvious nonlinear current. The potential distribution and band structure explain the mechanism for the anisotropy and nonlinearity. Then, based on calculation of the binding energy and Mulliken population, eight interface structures between graphene (GR) and ML α-GeTe were constructed, in which GC3 and TC3 were found to be relatively stable. Next, GR/ML α-GeTe/GR was established based on the two interfaces (GC3 and TC3). The current–voltage (IV) characteristics were calculated to show that the device has bipolar resistance characteristics, suitable set and reset voltages and a high window value (104). Further analysis of electron density inferred that the resistance mechanism was based on the drift of Te vacancies forming conductive filaments. And the performance of GR/ML α-GeTe/GR was found to be improved by the creation of Te vacancies. This work indicates that GR/ML α-GeTe/GR has the potential to be used to build resistive random access memory (RRAM) with good performance and may be instructive and valuable for the manufacture and application of RRAM.