We investigate the effects of nitrogen passivation on band structure and density of states in zigzag graphene nanoribbon (zzGNR) using first principle quantum mechanical simulations. The results show that nitrogen edge termination of zzGNR produces a bandgap (~0.7eV) around the Fermi level. We analyze the Bloch functions and projected density of states for understanding the origin of the bandgap. Based on these findings, we propose a nitrogen-passivated zzGNR FET structure having n-type electrodes and p-type scattering region using nitrogen and boron doping, respectively. We simulate and analyze its current-voltage (I-V ) characteristics using DFT combined with NEGF formalism and device density of states (DDOS). We observe a new negative differential resistance phenomenon in GNR FET, which can be controlled by the variation of the potential applied at gate of the zzGNR FET. This device has potential applications in logic, high frequency, and memory devices.