We propose in this Letter a single-mode graphene-coated nanowire surface plasmon waveguide. The single-mode condition and modal cutoff wavelength of high order modes are derived from an analytic model and confirmed by numerical simulation. The mode number diagram of the proposed waveguide in the wavelength-radius space is also demonstrated. By changing the Fermi level of graphene, the performance of the proposed waveguide could be tuned flexibly, offering potential application in tunable nanophotonic devices.