@The gravitational potential profile in the central region of the galaxy cluster Abell 1060 was measured utilizing X-ray data from ASCA and ROSAT. The ASCA X-ray spectra, after correcting for the spatial response of the X-ray telescope, show an isothermal distribution of the intra-cluster medium (ICM) within at least about 12 Radius of the cluster center. The azimuthally averaged surface brightness profile from the ROSAT PSPC exhibits a central excess of the ICM density above an isothermal beta model. The ring-sorted ASCA GIS spectra and the radial surface brightness distribution from the ROSAT PSPC were simultaneously utilized to constrain the gravitational potential profile, under assumptions of the hydrostatic equilibrium and single-phased nature of the ICM. The ICM density profile was specified by analytic forms. The total mass distribution was found to be described by a profile with a central cusp together with a logarithmic radial slope of about 1.5. The universal dark halo profile proposed by Navarro, Frenk, and White (1996; 1997) was also consistent with the data. The King potential model, however, with a flat density core gave no acceptable solution to the data. Discussions are made concerning the estimated dark matter distribution in the central region of clusters and its nature.