The semirigid vibrating rotor target (SVRT) model has been applied to the study of the reaction of D+CH4 →CH3+HD using a time-dependent wave packet method. The energy dependence of the calculated reaction probability shows oscillatory structures similar to those observed in the abstraction reaction of H+H2, H+CH4 etc. We have also studied the influence of rotational and vibrational excitation of the reacting molecule (CH4) on reaction probability.The excitation of the H-CH3 stretching vibration gives significant enhancement of reaction probability, which rises significantly with the enhancement of rotational quantum number j. Finally, we have compared the cross section and the rate constant of the D+CH4 system with that of the H+CH4 system.