The dynamics for the D+CD4→CD3+D2reaction have been studied using reduced dimensionality quantum-mechanical theory. By the theory, the reactive polyatomic molecule CD4was treated as a diatomic molecule D—CD 3 , so the system can be treated as a linear atom_diatom reaction, reducing the sy stem to a four_dimensional scattering problem. In calculations, the Hamiltonian of the reaction system has been carried out using the time-dependent wave packet method, and the propagation of wave packets by the split-operator method. The semiempirical potential energy surface which has been developed by Jordan and Gi lbert is employed. The energy dependence of the calculated reaction probability shows oscillatory structures, similar to those observed in abstraction reactions H+H2, H+CH4,etc. The excitation of the stretching vib ration of reac tive molecule D—CD3gives a significant enhancement of reaction pro babilit y, the reaction threshold decreases with the enhancement of the vibrating excita tion. Detailed study of the influence of initial rotational states on reaction p robability shows a strong steric effect. The integral cross sections of translat ional energy for CD4at both v=0 and v=1 at ground rotational state show th at the vibrational excitation significantly enhances the reaction cross section. And the reaction threshold decreases by about 0.2eV, consistent with that of re action probability. The significant enhancement of the reaction probability of r eaction H+CH4at ground state when compared with D+CD4 can be explain ed reasonably in terms of quantum mechanical zero-point energies and the tunneli ng effect.