Time-independent quantum scattering calculations have been performed to study the H+CH4--> H-2+CH3 reaction, using the analytic potential-energy surface developed by Jordan and Gilbert. A rotating bond umbrella (RBU) approximation with the implementation of a guided spectral transform subspace iteration technique has been applied together with a log-derivative method in hyperspherical coordinates. A single sector hyperspherical projection method was used to apply the boundary conditions to extract the S matrix at a large hyperradius. The results show that the H+CH4--> H-2+CH3 reaction occurs via a direct mechanism. The tunneling effect is pronounced, while there is little recrossing. Vibrational excitation of the C-H stretch and/or the H-CH3 bending modes of CH4 significantly enhance the reactivity. Exciting the umbrella mode of CH4 also enhance the reactivity, although less efficiently. The calculated thermal rate constants are larger than the experimental ones. However, good agreement has been obtained by including a barrier height correction of the potential function to make it agree with ab initio results. Finally, vibrational and rotational distributions of the reaction products are discussed in detail.