In this study, we investigate fusion cross sections including halo and weakly-bound nuclei around Coulomb barrier. We reviewed our previous results for the total fusion cross sections of the 66He+ 209209Bi, 1111Li+ 208208Pb and 14,1514,15C+ 232232Th systems, which involve well-known halo nuclei. Then, to analyze the total fusion reaction of neutron-rich nuclei, 99Li + 7070Zn system, we introduced the coupled channel method for a two-neutron transfer in the fusion reaction practically. To study the neutron-rich projectile nucleus of this system (99Li), we constructed a folding potential with projectile and target densities using charge density distribution. Finally, we analyzed the fusion cross section of the 99Li + 7070Zn system in one or two channel coupled manners. By adjusting the coupling strength and effective Q-value of the coupling form factor, we successfully reproduced the experimental fusion cross-section data for this system. Our results indicate that the two-neutron transfer channel plays a critical role in the fusion reactions of neutron-rich nuclei, such as 99Li nuclei at energies around the Coulomb barrier.