As an important secondary explosive, cyclotrimethylenetrinitramine (RDX, C3H6O6N6) is extensively used in military and industrial applications due to its high energy density and low sensitivity to external stimulations. Considerable attention has been devoted to the study of the detonation initiation, with particular interest in the mechanism by which energy is transferred from a shock wave to the internal molecular vibrations so as to begin endothermic decomposition. During the whole process, phonons as the primary carriers of heat may play an important role. Experimentally, inelastic neutron scattering (INS) technique provides a means of studying the dynamics of motions of atoms and molecules in the crystal, especially in the low frequency region which contains most phonon lattice modes. In this work, neutron diffraction pattern of polycrystalline RDX under ambient condition has been measured and compared with the calculated results, showing reasonable agreement with and thus confirming the structure of RDX. Subsequently, the vibrational INS spectrum of RDX has been measured at T=10 K over the region of 10-104~cm-1 by using cold neutron triple-axis spectrometer. On the basis of the solid-state density functional calculations with the generalized gradient approximation (BLYP and BP functionals), it is possible to perform normal-mode analysis, which agrees with previous assignments. A total of 9 phonon lattice modes and 3 internal vibrations have been identified. Eight possible doorway modes may be predicted in the energy range between 100 and 148~cm-1, which arise from the combinations of phonon lattice modes 38.3, 40.3, 50.2, 61.5~cm-1 and fundamental vibrations 86.6, 88.6, 101.4~cm-1. The doorway modes are the proposed bridge by which the energy of initial shockwave can pass from the external degrees of freedom into those of the molecule. It is shown that all of these eight modes have fundamental vibrational components that consist of nitro-group deformation vibrations. This point is of particular importance and supports the theory that the initial bond broken in detonation is the NN bond. This work may shed light on the mechanism of detonation initiation from a microscopic viewpoint.