The initial state selected time-dependent wave packet method has been developed to study the H-2 + CH3 -> H + CH4 reaction, by employing the seven and eight-dimensional models proposed by Palma and Clary in which the nonreacting CH3 moiety is restricted in C-3 nu symmetry. Total reaction probabilities and integral cross sections were calculated for the ground and a number of vibrationally excited initial states to investigate the effects of vibrational excitations of both reagents on the reaction. The eight-dimensional calculations showed that the CH stretching excitation does not have any important effect on the reaction and the seven-dimensional model with the CH bond length fixed works very well for the reaction. The excitation of H-2 vibrations could enhance the reaction but is less effective than the translation in the low energy region. In contrast, the first umbrella excitation is very effective on reducing the reaction threshold. The calculated rate constants are found to be in good agreement with available experimental measurements and other theoretical results.