In this paper, a A-N potential is presented. The long and medium range parts of this potential are'given by the OBEP(k+r)+w-r\'+) and TBEP'(2it+ir'p), while the. short range part by a phenomenological soft core. Based:on the A-N potential, the Aseparation energies and the spectra of ^He and \H as well as the s-wave phase shifts and the cross section of the A-N elastic scattering are calculated . The results are in good agreement '.with the experimental data. Finally, the A-well depth in nuclear matter is discussed.