The density functional theory -DFT- at the theoretical level B3LYP/ 6-31G and ωB97-XD/6-31G in vacuum and in water was used for the study of the inclusion complex of Trans-Anethole (T-An) in to β-Cyclodexrin (β-CD) in two orientations A and B. The results indicate that the most favorable structure from an energetic point of view is when the propenyl group enters the cavity of the (β-CD) through its wide cavity, hence the methoxy group is positioned on the narrow side thereof with complete insertion of the benzene group. Donor-acceptor interactions between guest and host, studied using natural bonding orbital (NBO) analysis show the presence of weak and strong intermolecular hydrogen bonds in addition to van der Waals interactions. The spectral analysis of the 1HNMR proton discussed with NBO results confirm the mutual interactions between T-An. and (β-CD). Also, the comparison of the theoretical and experimental UV spectra showed a good agreement thus justifying the appropriateness of the theoretical process undertaken in the modeling of this inclusion complex as affirmed by infrared spectroscopy and NCI analysis.