The vortex structure is studied in light of MgB2 theoretically based on a two-band superconducting model by means of Bogoliubov-de Gennes framework. The field dependence of the electronic specific heat coefficient gamma(H) is focused. The exponent alpha in gamma(H) alphaH(alpha) is shown to become smaller by adjusting the gap ratio of the two gaps on the major and minor bands. The observed extremely small value alpha similar to 0.23 could be reasonable in this two-band model with the gap ratio similar to0.3.