Elastic scattering of the $^{6}$He + $^{12}$C system at 38.3 MeV/nucleon has been analyzed by extending the optical limit approximation to the Coulomb-modified Glauber model. Assuming that the $^{6}$He nucleus consists of a $^{4}$He core and two weakly-bound neutrons, we take the $^{6}$He density to be a sum of the densities of the core and the two halo neutrons. The calculated differential cross section, taking into account the halo effect, is found to be in fairly good agreement with the observed data. The oscillatory structure observed in the angular distribution can be explained as being due to the interference between the near-side and the far-side amplitudes. We investigate the halo neutrons' effects on the density, the angular distribution, the imaginary phase shift, the transparency function, and the reaction cross section. We found the introduction of the halo structure of $^{6}$He to be important in the description of $^{6}$He + $^{12}$C elastic scattering.

Keywords: Neutron-rich nucleus, Halo effect, Coulomb-modified Glauber model, Elastic scattering, Phase shift, $^{6}$He + $^{12}$C