An intumescent‐flame‐retardant vinyl acetate–ethylene copolymer (IFR/VAE) compound has been prepared by blending with a complex of melamine amino trimethyl phosphate (M‐AT) and sodium lignosulfonate (SL). Then, this obtained IFR/VAE polymer was applied as adhesives for producing the flame‐retardant plywood. The IFR VAE sample (VAE/M‐AT3/SL1) with a mass ratio 3:1 (M‐AT to SL) showed an enhanced amount of char residue, limiting oxygen index (LOI) value and tensile strength value to 20.6 wt%, 32 vol% and 19.3 MPa, which have been increased by 796%, 600%, and 56% compared to that of neat VAE. The cone calorimeter result showed that the peak of heat release rate (pHRR) of VAE/M‐AT3/SL1 sample was reduced by 48% compared to the control one. Additionally, the second peak of HRR of sample IFRPW/15 L/15 (containing 15 wt% M‐AT3/SL1 in the plywood adhesive layer) presented a reduction of 29% compared to that of the sample PW/15 L (neat plywood). It is assigned to the formation of phospho‐carbonaceous structure during combustion, thus the flame‐retardancy of plywood has been greatly enhanced. Thus, this work provides an economical and applicable fire‐retardant VAE adhesive formula for producing plywood materials with good performances.