A report is presented on Suzaku observations of the ultra-luminous X-ray source X-1 in the starburst galaxy M82, made three time in 2005 October for an exposure of ~ 30 ks each. The XIS signals from a region of radius 3 around the nucleus defined a 2-10 keV flux of 2.1 x 10^-11 erg s-1 cm-2 attributable to point sources. The 3.2-10 keV spectrum was slightly more convex than a power-law with a photon index of 1.7. In all observations, the HXD also detected signals from M82 up to ~ 20 keV, at a 12-20 keV flux of 4.4 x 10^-12 erg s-1 cm-2 . The HXD spectrum was steeper than that of the XIS. The XIS and HXD spectra can be jointly reproduced by a cutoff power-law model, or similar curved models. Of the detected wide-band signals, 1/3 to 2/3 are attributable to X-1, while the remainder to other discrete sources in M82. Regardless of the modeling of these contaminants, the spectrum attributable to X-1 is more curved than a power-law, with a bolometric luminosity of (1.5 -3) x 10 ^40 erg s-1. These results are interpreted as Comptonized emission from a black hole of 100-200 solar masses, radiating roughly at the Eddington luminosity.