Cosmic-ray proton and helium spectra have been measured with the balloon-borne Cosmic Ray Energetics And Mass experiment flown for 42 days in Antarctica in the 2004-2005 austral summer season. High-energy cosmic-ray data were collected at an average altitude of ~38.5 km with an average atmospheric overburden of ~3.9 g cm--2. Individual elements are clearly separated with a charge resolution of ~0.15 e (in charge units) and ~0.2 e for protons and helium nuclei, respectively. The measured spectra at the top of the atmosphere are represented by power laws with a spectral index of --2.66 ? 0.02 for protons from 2.5 TeV to 250 TeV and --2.58 ? 0.02 for helium nuclei from 630 GeV nucleon--1 to 63 TeV nucleon--1. They are harder than previous measurements at a few tens of GeV nucleon--1. The helium flux is higher than that expected from the extrapolation of the power law fitted to the lower-energy data. The relative abundance of protons to helium nuclei is 9.1 ? 0.5 for the range from 2.5 TeV nucleon--1 to 63 TeV nucleon--1. This ratio is considerably smaller than the previous measurements at a few tens of GeV nucleon--1.