We present a numerical study of the effect of interstitial air on a vertically vibrated granular bed within one period of oscillation. We use a three-dimensional molecular-dynamics simulation including air phenomenologically. The simulations are validated with experiments made with spherical glass beads in a rectangular container. After validation, results are reported for a granular column of 9000 grains and approximately 50 layers deep (at rest), agitated with a sinusoidal excitation with maximal acceleration 4.7g at 11.7 Hz. We report the evolution of density, granular temperature, and coordination number within a vibration cycle, and the effect of interstitial air on those parameters. In three-dimensional computer simulations we found that the presence of interstitial air can promote the collective motion of the granular material as a whole.