γ-Glu-Val-Gly (γ-EVG) is a potent kokumi peptide that can be synthesized through the transpeptidase reaction catalyzed by γ-glutamyl transferase from bovine milk (BoGGT). To explore the molecular mechanism between BoGGT and l-glutamine, γ-glutamyl peptides were generated through the transpeptidase reaction catalyzed by BoGGT at various reaction conditions. Quantitation of γ-glutamyl peptides, structure prediction of BoGGT, molecular docking, and molecular dynamic simulations were performed. Membrane-free BoGGT had a higher transpeptidase activity with Val-Gly as an acceptor than membrane BoGGT. The suitable conditions for γ-EVG production using BoGGT were 100 mM Val-Gly, 20 mM Gln, 1.2 U/mL BoGGT, pH 8.5, and 37 °C, and 13.1 mM γ-EVG was produced. The hydrogen bonds are mainly formed between residues from the light subunit of BoGGT (Thr380, Thr398, Ser450, Ser451, Met452, and Gly473) and the l-glutamine donor. NaCl might inhibit the transpeptidase activity by destroying the hydrogen bonds between BoGGT and l-glutamine, thereby increasing the distance between the hydroxyl oxygen atom on Thr380 of BoGGT and the amide carbon atom on l-glutamine.