Recent studies of thermal transport in nanomaterials have demonstrated the breakdown of Fourier's law through observations of ballistic transport. Despite its unique features, another instance of the breakdown of Fourier's law, hydrodynamic phonon transport, has drawn less attention because it has been observed only at extremely low temperatures and narrow temperature ranges in bulk materials. Here, we predict on the basis of first-principles calculations that the hydrodynamic phonon transport can occur in suspended graphene at significantly higher temperatures and wider temperature ranges than in bulk materials. The hydrodynamic transport is demonstrated through drift motion of phonons, phonon Poiseuille flow and second sound. The significant hydrodynamic phonon transport in graphene is associated with graphene's two-dimensional features. This work opens a new avenue for understanding and manipulating heat flow in two-dimensional materials.