To eliminate toxic formaldehyde from wood-based panels, a new formaldehyde-free wood adhesive (named OL/PEI adhesive) was synthesized by a reaction of oxidized lignin (OL) and polyethylenimine (PEI) reaction in the presence of sodium periodate. The curing mechanism of the OL/PEI adhesive was clarified by Fourier transform infrared spectroscopy (FTIR) and solid-state cross-polarization magic angle spinning carbon-13 nuclear magnetic resonance (CP/MAS13C-NMR) spectroscopy. The results showed that the sodium periodate could selectively oxidize wheat straw lignin to produce the ortho-quinone, and then the ortho-quinone in OL could further react with amino groups in PEI to form the OL/PEI adhesive. The as-prepared poplar particleboard was investigated with regard to hot-pressing temperature, the hot-pressing time, the OL/PEI weight ratio, and the dosage of OL/PEI adhesive. Under the optimum conditions, e.g., hot pressing temperature of 180 °C, hot pressing time of 13 min, the OL/PEI weight ratio of 1:1, and the dosage of 10%, OL/PEI adhesive was found to disperse evenly into the voids among the shavings of poplar particleboard, followed by the curing of OL/PEI adhesive using hot-pressing to form tightly bonds between the shavings. The resulting particleboard reached the requirement of mechanical properties (GB/T 4897.3-2003), higher water resistance properties, and better heating resistivity. This study demonstrated a new way to produce a formaldehyde-free wood adhesive with unique properties. This material could replace formaldehyde wood adhesive in wood bonding.