The structures, energetics, and binding characteristics of complexes formed between anisole (C6H5OCH3) and boron trifluoride (BF3) were investigated using MP2 and B3LYP methods with 6-31+G(d,p) and 6-311 +G(d,p) basis sets. Among the complexes with a 1: 1 ratio of C6H5OCH3 to BF3, both B3LYP and MP2 methods predict the same structures and relative stability of the isomers; however, the B3LYP binding energies are smaller than the MP2 energies. Furthermore, the weaker the interaction, the greater the discrepancy in binding energy. The charge decomposition analysis (CDA) showed that there are two types of complexes: the Lewis acid-base adduct and the van der Waals complexes. The CDA results also illustrated that there is a significant donation from the oxygen lone pair electrons to the boron vacant orbital in the adduct. The van der Waals complexes were formed through the aromatic ring and BF3 interaction or through the H and F interactions. The MP2 results showed that the formation of adduct at room temperature is thermodynamically favorable. Among the 1:2 C6H5OCH3-BF3 complexes, the most stable structure consists of both the Lewis acid-base and van der Waals binding; i.e., one BF3 binds with C6H5OCH3 to form C6H5OCH3-BF3 adduct, while the other BF3 binds with this adduct through van der Waals interactions. The calculated binding energy of the 1: 1 complex is close to the experimental heat of formation, which suggests that the 1:1 complexes are the most likely species in the C6H5OCH3 and BF3 mixture.