The molecular mechanism for the cycloaddition reaction between 2-methylfuran and acetylenedicarboxylic acid (ADA) has been characterized using density functional theory methods at the B3LYP/6-31+G* theory level. An analysis of the results on the reaction pathway shows that the reaction takes place along a stepwise mechanism. The initial step corresponds to the nucleophilic attack of the C5 position of the furan ring to one carbon atom of the conjugated acetylenic system of ADA to give a zwitterionic intermediate. Closure of this intermediate along the nucleophilic attack of the other acetylenic carbon to the substituted C2 position of the furan ring affords the Diels-Alder cycloadduct. Although the B3LYP/6-31G* calculations afford good potential energy barriers, the inclusion of diffuse functions is required in order to obtain a complete characterization of the molecular mechanism.