The dynamics for the H+CH4-->H-2+CH3 reaction has been studied using reduced dimensionality quantum-mechanical theory. The system is treated as a linear four-atom chemical reaction, reducing the system to a three-dimensional scattering problem. The vibrational modes of nu(1) and nu(4) of CH4, the stretching vibration of H-2, and the umbrella nu(2) mode of CH3 are taken into consideration in the reaction dynamics based on the vibrational analysis along the reaction path. The,semiempirical potential energy surface which has recently been developed by Jordan and Gilbert [J. Chem. Phys. 102, 5669 (1995)] is employed. Rotationally averaged cross sections and thermal rate constants are calculated using an energy-shifting approximation in order to take into account the effect of all the degrees of freedom. It is shown that excitation of the nu(1) mode of CH4 significantly enhances the reactivity, indicating that there is a strong coupling between the nu(1) mode of CH4 and the reaction coordinate. The vibrational state distributions for the products H-2 and CH3 have also been studied. In the energy range considered here, the population of vibrationally excited H-2 is found to be very small, while the umbrella nu(2) mode of CH3 is found to be excited.