Plant protein adhesive has received considerable attention because of their renewable raw material and no harmful substances such as formaldehyde. However, for the plant protein adhesive used in the field of plywood, low cost, strong water resistance, and high bonding strength were the necessary conditions for practical application. In this work, a double-network structure including hydrogen bonds and covalent bonds was built in hot-pressed peanut meal (HPM) protein (HPMP) adhesive, soybean meal (SBM) protein (SBMP) adhesive and cottonseed meal (CSM) protein (CSMP) adhesives. The ether bonds and ester bonds were the most in CSMP adhesive, followed by SBMP adhesive, while the hydrogen bond was the most in HPMP adhesive. The solubility of the HPMP, SBMP, and CSMP adhesives decreased by 14.3%, 24.2%, and 19.4%, the swelling rate decreased by 56.9%, 48.4%, and 78.5%, respectively. The boiling water strength (BWS) of HPMP (0.82 MPa), SBMP (0.92 MPa), and CSMP adhesives reached the bonding strength requirement of China National Standards class I plywood (type I, 0.7 MPa). The wet shear strength (WSS) of HPMP, SBMP, and CSMP adhesives increased by 334.5% (1.26 MPa), 246.3% (1.42 MPa), and 174.1% (1.59 MPa), respectively. This study provided a new theory and method for the development of eco-friendly plant meal protein adhesive and promotes the development of green adhesive.