Using a first-principles approach, we study the vibrational properties of vitreous SiO2 which are measured in neutron-scattering experiments. We adopt a model structure consisting of corner-sharing tetrahedra, which was previously generated using first-principles molecular dynamics. We calculate the dynamic, structure function S(q,E) as a function of wave vector q and energy E by taking explicitly into account the correlations between different atoms as given by the normal modes. The effects of temperature and finite displacements are also considered. Overall, the agreement with experiment is very good, as illustrated by the comparison for the density of states. However, the calculated and measured S(q,E) differ in some cases up to a factor of 2 in absolute intensity. Nevertheless, the oscillations in S(q,E) describing the correlations between the motions of the atoms are accurately reproduced. The neutron effective density of states obtained directly from S(q,E) yields a good representation of the actual density of states. By introducing a comprehensive scheme, we clarify the relation between neutron and infrared spectre. In particular, we show that the neutron density of states does not distinguish between longitudinal and transverse excitations. Other properties such as the mean-square displacements and the elastic structure factor are also evaluated and found to be in good agreement with experiment.