We investigate the electron-phonon coupling and mean-free path in zigzag edge graphene nanostrips (GNSs). Our calculations show both expected similarity with armchair single-wall carbon nanotubes (SWNTs) and suppression of the electron-phonon scattering due to localized edge states. Low-energy acoutic phonon scattering is exponentially small at room temperature due to a large wavevector separation of the scattering channels. Our calculations yield an electron-phonon mean-free path that is proportional to the width of the nanostrip and is of the order of tens of micrometers.