The $^{12}C+^{12}C$ reaction is one of the most important reactions in the evolution of massive stars. The cross-section and the astrophysical S factor were calculated using the potential of AW95 and the new optimized potential. The new optimized potential in reproducing the fusion cross section and astrophysical S factor is very successful at low energies, also the hindrance and maximum in S factor is visible in this same energy range and is in good agreement with the experimental results. But at higher energies, the results obtained using the AW95 potential are in better agreement with the experimental results. However, it is appropriate to use this new potential to reproduce the barrier phenomenon and the experimental results at low energies, which are more important in astrophysics. The S-factor, obtained in the coupled channel calculation for the $^{12}C+ ^{12}C$ reaction, had a maximum value at energy near 3.6 MeV.
