A new decomposition of the Dirac Brückner-Hartree-Fock (DBHF) G matrix is used to study the isospin-dependent relativistic microscopic optical potential (RMOP). The optical potential of finite nuclei can be obtained in the local den sity approximation. The energy dependence of proton-nucleus scattering for the optical potentials of finite nuclei is discussed. The differential cross section s and the resolution power in the p+4040Ca and p+208208Pb at Epp less than 200MeV are also calculated using the above RMOP. I t is found that the calculated results agree with the experimental results. It should be e mphasized that the ROMP obtained from DBHF G matrix without any free parameter s could well describe the proton elastic scattering. This RMOP can also be used for unstable nuclei. From the results of the Ca isotopes, it is found that the i sospin dependence is more important for the exotic nuclei.