A parameter-independent microscopic optical potential of nucleus-nucleus interaction is presented by a folding model with the isospin dependent complex nucleon-nuclear potential, which is calculated in the framework of the Dirac-Bruecker-Hartree-Fock approach. Investigations on 6Li scattering by 12C, 28Si, 40Ca, 58Ni, 90Zr, and 208Pb over a wide range of incident energy and scattering angle with the microscopic nucleus-nucleus optical potential is presented. To take account of the breakup effect of 6Li and the high order dynamic effect in the reaction a modification factor NR in the real part and an enhancing factor NI in the imaginary part of the microscopic optical potential are introduced. We take the imaginary part enhancing factor NI=3.0, which has been obtained in the previous study on 6He scattering by 12C. The modification factor NR is found to be almost constant with respect to the incident energy and target mass number. The calculations with NR≈0.5—0.6 and NI=3.0 well reproduce the experimental elastic scattering data for all targets and incident energies investigated. Our parameter-independent model should be of value in the description of the nucleus-nucleus scattering of many-body systems, especially unstable nucleus-nucleus systems.