We report on the spectral evolution of a new X-ray transient, MAXI J0556-332, observed by MAXI, Swift, and RXTE. The source was discovered on 2011 January 11 (MJD=55572) by MAXI Gas Slit Camera all-sky survey at (l,b)=(238.9deg, -25.2deg), relatively away from the Galactic plane. Swift/XRT follow-up observations identified it with a previously uncatalogued bright X-ray source and led to optical identification. For more than one year since its appearance, MAXI J0556-332 has been X-ray active, with a 2-10 keV intensity above 30 mCrab. The MAXI/GSC data revealed rapid X-ray brightening in the first five days, and a hard-to-soft transition in the meantime. For the following ~ 70 days, the 0.5-30 keV spectra, obtained by the Swift/XRT and the RXTE/PCA on an almost daily basis, show a gradual hardening, with large flux variability. These spectra are approximated by a cutoff power-law with a photon index of 0.4-1 and a high-energy exponential cutoff at 1.5-5 keV, throughout the initial 10 months where the spectral evolution is mainly represented by a change of the cutoff energy. To be more physical, the spectra are consistently explained by thermal emission from an accretion disk plus a Comptonized emission from a boundary layer around a neutron star. This supports the source identification as a neutron-star X-ray binary. The obtained spectral parameters agree with those of neutron-star X-ray binaries in the soft state, whose luminosity is higher than 1.8x10^37 erg s^-1. This suggests a source distance of >17 kpc.