Using a combination of non-equilibrium Green's function (NEGF) and density functional theory (DFT), the electronic structures and transport characteristics of N-doped GeSe monolayer were investigated systematically. The calculated band structures illustrated that the doping of N atoms changed GeSe monolayer from a semiconductor to a metal. Further, a clear negative differential resistance behavior (NDR) was found in the voltage-current curves of the N-doped GeSe based devices. Moreover, the current peak-to-valley ratio (PVR) varied with the doping concentration of N atoms. As the doping concentration decreased, the peak of NDR shifted toward the millivolt region. Especially, the NDR behavior with a PVR up to 103 entered the mV bias region when the doping concentration was reduced to 0.69%. These results provide a novel approach to design the low power nanodevice based on the GeSe monolayer. [ABSTRACT FROM AUTHOR]