We theoretically study the plasmon modes in double parallel metallic armchair graphene nanoribbons (AGNRs) separated by a distance Lb. Starting with a single doped metallic AGNR at zero temperature, we show the plasmon dispersion dependence on the Fermi wave vector. By evaluating the static dielectric function for this ribbon, we find that the usual logarithmic divergence at q=2kF is absent. This indicates that plasmons in metallic AGNRs might be the most robust charge-density oscillations occurring in quasi-one-dimensional electron systems. We also study the influence of the distance Lb and of the carrier densities on the out-of-phase and in-phase plasmon modes. Finally, we address the intra-intersubband electron-hole transitions in single metallic armchair ribbons and find a strong influence of doping on the intrasubband plasmon modes. © 2013 American Physical Society.