Phonon transport in two-dimensional materials has been the subject of intensive studies both theoretically and experimentally. Recently observed unique phenomena such as Poiseuille flow at low temperature in graphene nanoribbons (GNRs) initiated strong interest in similar effects at higher temperatures. Here, we carry out massive molecular dynamics simulations to examine thermal transport in GNRs at room temperature (RT) and demonstrate that non-diffusive behaviors including Poiseuille-like local thermal conductivity and second sound are obtained, indicating quasiballistic thermal transport. For narrow GNRs, a Poiseuille-like thermal conductivity profile develops across the nanoribbon width, and wider GNRs exhibit a mixed nature of phonon transport in that diffusive transport is dominant in the middle region whereas non-uniform behavior is observed near lateral GNR boundaries. In addition, transient heating simulations reveal that the driftless second sound can propagate through GNRs regardless of the GNR width. By decomposing the atomic motion into out-of-plane and in-plane modes, it is further shown that the observed quasiballistic thermal transport is primarily contributed by the out-of-plane motion of C atoms in GNRs.