Wood adhesives fabricated from biomass can substitute formaldehyde-based ones, reducing the consumption of fossil resources and eliminating formaldehyde pollution. In this study, a novel and sustainable water-soluble soybean polysaccharide (WSSPS)-based adhesive is designed. Specifically, a hyperbranched aminated polysaccharide (HBPA-g-WSSPS), as an adhesive matrix, is synthesized via grafting reaction between oxidized WSSPS and hyperbranched polyamide (HBPA). Triglycidylamine, a bio-based epoxide cross-linker, reacted with the HBPA-g-WSSPS to afford a cross-linked hyperbranched network, providing strong cohesion for the adhesive. Additionally, polyacrylamide imparted an adjustable viscosity to the adhesive. The resultant WSSPS-based adhesive enhanced the wet shear strength of plywood (1.24 MPa) by 49% compared to the E-0-level industrial-use melamine-urea-formaldehyde (MUF) resin and by 26% compared to the industrial-use soybean meal/polyamidoamine-epichlorohydrin (PAE) adhesive. In addition, the adhesive has characteristics similar to those of the MUF resin, including viscosity, coating performance, hot-pressing conditions, and dry bond strength, which are superior to those of the soybean meal/PAE adhesive. This developed polysaccharide-based adhesive can potentially enhance various composites and can be used in industrial sectors.