This paper proposes a new hybrid method combining the Monte Carlo (MC) method and the Method of Characteristics (MOC). The hybrid method employs MC and MOC together to solve a neutron transport problem. The two different methods are applied to different neutron energy ranges. The MC method is used to obtain accurate solutions in the resonance energy range, and the MOC is used for high and low neutron energy ranges to achieve high performance of the new method. The two methods are consistently coupled through scattering and fission source terms during the power iterations and group sweepings. Numerical tests with a model problem confirm that the hybrid method can produce a more accurate solution than a conventional MOC by a factor of 10 and much higher computational efficiency than a conventional MC method by a factor of 90.