An analytical model for plasmon modes in graphene-coated dielectric nanowire is presented. Plasmon modes could be classified by the azimuthal field distribution characterized by a phase factor exp(imφ) in the electromagnetic field expression and eigen equation of dispersion relation for plasmon modes is derived. The characteristic of plasmon modes could be tuned by changing nanowire radius, dielectric permittivity of nanowire and chemical potential of graphene. The proposed model provides a fast insight into the mode behavior of graphene-coated nanowire, which would be useful for applications based on graphene plasmonics in cylindrical waveguide.