The elastic scattering angular distributions of the 6Li + 58Ni reaction are reanalyzed by using the double-folding model (DFM) within the framework of the optical model (OM) at energies near the Coulomb barrier, ELab = 9.9, 11.2, 12.1, 13.0 and 14.0 MeV. With this goal, for the first time, the no-core full configuration (NCFC) density distribution (DD) of the 6Li nucleus is used in order to obtain the real potentials. Also, in order to see the validity of NCFC DD, another density distribution (Gaussian shape) of the 6Li nucleus is used to obtain the real potentials in DF calculations. The results with NCFC DD are compared with Gaussian shape (GS) DD as well as the experimental data. It has been seen that the NCFC DD results are in agreement with the experimental data, giving better results than GS DD.