Polycarboxylic acids have been used as cross-linking agents for cellulose to increase the wet strength of paper. In this research, we applied Fourier transform infrared (FT-IR) spectroscopy to study the kraft paper treated with poly(maleic acid) and 1,2,3,4-butanetetracarboxylic acid. FT-IR spectroscopy is used to measure the carboxyl of a polycarboxylic acid and ester on the treated paper. The ester carbonyl band intensity and the carbonyl band intensity ratio (ester/carboxylate) are used for the evaluation of the effectiveness of a polycarboxylic acid for crosslinking cellulose on the paper. The correlation between the ester carbonyl band intensity and the wet strength improvement of the treated paper reveals that the increase in the paper wet strength by a polycarboxylic acid is the result of ester cross-linking of cellulosic fibers and molecules. We identified a five-membered cyclic anhydride intermediate formed on the paper during the curing processes. The infrared spectroscopy data support the reaction mechanism that a polycarboxylic acid esterifies cellulose through the formation of a five-membered cyclic anhydride as a reactive intermediate. We also studied the catalysis effects of sodium hypophosphite on the formation of the anhydride intermediate and the esterification of wood cellulose by a poly(carboxylic acid).