In this paper, a non-Hermitian graphene plasmonic waveguide system is proposed in the mid-infrared region. The proposed structure consists of two resonators and a graphene waveguide, which are attached to the SiO2 substrate. Based on the far-field coupling between the two stub plasmonic resonators, the single-band unidirectional reflectionless phenomenon of fundamental edge plasmonic mode in the non-Hermitian waveguide system has been theoretically studied. It can be found that when plasmonic mode is incident from one side, the reflection is 0, but from the other side, the reflection is 26.212%, so an exceptional point (EP) appears. Furthermore, the EP blueshifts with increasing Fermi level, and is unchanged under different relaxation times. All the simulation results are conducted by finite element method. Therefore, our findings pave a new way for the development of terahertz sensors, diodes, and so on.