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Using \gamma -ray beams produced in the inverse Compton scattering between \CO_2 laser photons and relativistic electrons, we have calibrated electron beam energies in the nominal energy range 550–974 MeV at the synchrotron radiation facility NewSUBARU. The laser Compton-scattering (LCS) \gamma -ray beams were produced at energies from 561  to 1728 keV and detected with a high-purity germanium detector. The electron beam energies were determined by reproducing the full energy peaks of the \gamma -ray beams by Monte Carlo simulations. The accuracy of the calibration is (5.5 - 9.4) \times 10^ - 5. The reproducibility of the electron beam energy is excellent in an independent injection and deceleration. The present energy calibration of the electron beams offers a standard for the energy calibration of high-energy LCS \gamma -ray beams produced with a \Nd:YVO_4 laser. As applications of the energy calibration, we investigated the energy linearity of a 3.5^\prime\prime \times 4.0^\prime\prime \LaBr_3(\Ce) detector in the response to \gamma -rays at energies up to 10 MeV and the energy profile of the high-energy LCS \gamma -ray beams. [ABSTRACT FROM AUTHOR]