A ${eta}$-glucosidase with the molecular mass of 160,000 Da was purified to homogeneity from cell extract of a cellulolytic bacterium, Cellulomonas uda CS1-1. The kinetic parameters ($K_m$ and $V_{max}$) of the enzyme were determined with pNP-cellooligosccharides (DP 1-5) and cellobiose. The molecular orbital theoretical studies on the cellulolytic reactivity between the pNP-cellooligosaccharides as substrate (S) molecules and the purified ${eta}$-glucosidase (E) were conducted by applying the frontier molecular orbital (FMO) interaction theory. The results of the FMO interaction between E and S molecules verified that the first stage of the reaction was induced by exocyclic cleavage, which occurred in an electrophilic reaction based on a strong charge-controlled reaction between the highest occupied molecular orbital (HOMO) energy of the S molecule and the lowest occupied molecular orbital (LUMO) energy of the hydronium ion ($H_3O^+$), more than endocyclic cleavage, whereas a nucleophilic substitution reaction was induced by an orbital-controlled reaction between the LUMO energy of the oxonium ion ($SH^+$) protonated to the S molecule and the HOMO energy of the $H_2O_2$ molecule. A hypothetic reaction route was proposed with the experimental results in which the enzymatic acid-catalyst hydrolysis reaction of E and S molecules would be progressed via $SN_1$ and $SN_2$ reactions. In addition, the quantitative structure-activity relationships (QSARs) between these kinetic parameters showed that $K_m$ has a significant correlation with hydrophobicity (logP), and specific activity has with dipole moment, respectively.