In this work, we propose a hierarchy of macroscopic models for the description of phonon transport in graphene. They are devised starting from the phonon Boltzmann transport equation by using the moments method and the maximum entropy principle. The state variables are the phonon energy densities and the fluxes of integer powers of the energy. We underline that the full energy dispersion relations are used. We test the validity of the models by analysing the steady-state and dynamical thermal conductivity, and the heat transport in zigzag and armchair graphene nanoribbons under a fixed temperature gradient.