Novel soybean meal-based biomimetic (STP) adhesives were fabricated via soybean meal (SM) and enhanced by tannic acid (TA) and polyetheylenimine (PEI) (TAPI) co-crosslinking network based on natural polyphenol-inspired chemistry. The multiple physico-chemical interactions (including intermolecular H-bonding and covalent bonding) between the TAPI co-crosslinking system and SM matrices were examined by the Fourier transform infrared spectroscopy, solid-state 13C nuclear magnetic resonance, X-ray diffraction, thermogravimetric analysis, and scanning electron microscopy. The results showed that a dense, robust, and water-resistant adhesive layer was constructed between network-bound catechol moieties in the TAPI and SM system, endowing the STP adhesive with high wet bonding strength for plywood. As expected, TAPI-modified SM adhesives showed a 156.1% increase in wet bonding strength compared to the control SM adhesive. The adhesion meets standard requirements for interior-use plywood. Both the solid content and residual mass analysis also confirmed that the enhancement in the STP adhesive was attributable to the network crosslinking density and stiffness after integrating the TAPI system. Moreover, the thermal stability of the resultant STP adhesive exhibited a significant improvement. The proposed STP adhesive may be a promising cost-effective and wet-resistant bio-adhesive for the application in the wood composites industry.