A theoretical study on the rotational dynamics of H2 molecules trapped in the interstitial channels (ICs) of a carbon nanotube bundle is presented. The potential used in this study is modeled as a sum of atom-atom (C-H) van der Waals interactions and electrostatic interactions of the molecule with the surrounding nanotubes.The rotational energy spectra is calculated using a product wave function, where the coupling between translational and rotational modes is treated in a mean-field manner . Molecular dynamics (MD) simulation study was performed for estimating the hydrogen rotational barrier. Both theoretical calculations and simulation results reveal the existence of a large rotational barrier (~ 40 meV). The consequences of this rotational barrier for the rotational energy levels are worked out in detail.