Molybdenum disulfide (MoS2) among two-dimensional semiconductor films is promising for spintronic devices because it has a longer spin-relaxation time with contrasting spin splitting than silicon. However, it is difficult to fabricate integrated circuits by the widely used exfoliation method. Here, we investigate the contact characteristics in the Fe/Al2O3/sputtered-MoS2 system with various thicknesses of the Al2O3 film. Current density increases with increasing thickness up to 2.5 nm because of both thermally-assisted and direct tunneling currents. On the other hand, it decreases with increasing thickness over 2.5 nm limited by direct tunneling currents. These results suggest that the Schottky barrier width can be controlled by changing thicknesses of the Al2O3 film, as supported by calculations. The reduction of conductance mismatch with this technique can lead to highly efficient spin injection from iron into the MoS2 film.