We have measured the Hall resistivity (${ ho}_{xy}$) and the longitudinal resistivity (${ ho}_{xy}$) on superconducting $MgB_2$ thin films in extended fields up to 18 T. We found a universal scaling behavior between the Hall resistivity and the longitudinal resistivity, which is independent of the temperature and the magnetic field. At a wide magnetic field region from 1 to 18T, a universal power law of ${eta}=2.0{pm}0.1$ in a scaling relation, ${ ho}_{xy}={A{ ho}_{xx}}^{eta}$, was observed in c-axis-oriented $MgB_2$ thin films. These results can be well interpreted by using recent models.