Nonreciprocal photonic devices enable “one-way” light flows and are essential building blocks of optical systems. Here, we investigate an alternative paradigm to break reciprocity and achieve unidirectional subwavelength light propagation fully compatible with modern all-photonic highly integrated systems. In agreement with a few recent studies, our theoretical model predicts that a graphene sheet biased with a drift electric current has a strong nonreciprocal tunable response. Strikingly, we find that the propagation of the surface plasmon polaritons can be effectively “one-way” and may be largely immune to the backscattering from defects and obstacles. Furthermore, the drift-current biasing may boost the propagation length of the graphene plasmons by more than 100%. Our findings open new inroads in nonreciprocal photonics and offer a new opportunity to control the flow of light with one-atom thick nonreciprocal devices.