One of the main interests in the food industry is the preservation of food from spoilage by microorganisms or lipid oxidation. A novel alternative is the development of additives of natural origin with dual activity. In the present study, a chemically modified lysozyme (Lys) with epigallocatechin gallate (EGCG) was developed to obtain a conjugate (Lys-EGCG) with antibacterial/antioxidant activity to improve its properties and increase its application potential. The modification reaction was carried out using a free radical grafting method for the Lys modification reaction, using ascorbic acid and hydrogen peroxide as radical initiators in an aqueous medium. The synthesis of Lys-EGCG conjugate was confirmed by spectroscopic (FT-IR, 1H-RMN, and XPS) and calorimetry differential scanning (DSC) analyses. The EGCG binding to the Lys biomolecule was quantified by the Folin-Ciocalteu method; the antibacterial activity was evaluated by minimum inhibitory concentration (MIC) and minimum bactericidal concentration (MCB) against Staphylococcus aureus and Pseudomonas fluorescens; the antioxidant activity was evaluated by ABTS, DPPH, and FRAP. The spectroscopic results showed that the Lys-EGCG conjugate was successfully obtained, and the DSC analysis revealed a 20°C increase (P < 0.05) in the denaturation temperature of Lys due to EGCG modification. The EGCG concentration in Lys-EGCG was 97.97 ± 4.7µmol of EGCG/g of sample. The antibacterial and antioxidant activity of the Lys-EGCG conjugate was higher (P < 0.05) than pure EGCG and Lys. The chemical modification of Lys with EGCG allows for the bioconjugate with a dual function (antibacterial/antioxidant), broadening the range of Lys and EGCG applications to different areas such as food, cosmetic, and pharmaceutical industries.