We investigate the Dbar-N interaction at low energies using a meson-exchange model supplemented with a short-distance contribution from one-gluon-exchange. The model is developed in close analogy to the meson-exchange KN interaction of the Juelich group utilizing SU(4) symmetry constraints. The main ingredients of the interaction are provided by vector meson (rho, omega) exchange and higher-order box diagrams involving D*N, DDelta, and D*Delta intermediate states. The short range part is assumed to receive additional contributions from genuine quark-gluon processes. The predicted cross sections for Dbar-N for excess energies up to 150 MeV are of the same order of magnitude as those for KN but with average values of around 20 mb, roughly a factor two larger than for the latter system. It is found that the omega-exchange plays a very important role. Its interference pattern with the rho-exchange, which is basically fixed by the assumed SU(4) symmetry, clearly determines the qualitative features of the Dbar-N interaction -- very similiar to what happens also for the KN system.