We conducted computational research to investigate the mechanism by which cyclodextrins (CDs) catalyze Diels-Alder reaction between 9-anthracenemethanol and N-cyclohexylmaleimide. Hydrogen bonds between N-cyclohexylmaleimide and the hydroxyl groups of cyclodextrins were initially thought to play an important role in the catalysis [Chaudhuri, S. et al. Tetrahedron Letters, 2015, 56, 1619-1623 Our calculations show that such hydrogen bonds, if exist, could lower the activation energy barrier for the transition state of 9-anthracenemethanol and Ncyclohexylmaleimide to some extent. However, they are not stable enough to promote the reaction. The binding of 9-anthracenemethanol and N-cyclohexylmaleimide to cyclodextrins is found to be the key to the catalysis. Cyclodextrins act as a container to hold the two reactants in the cavity, pre-organizes them for the reactions, and thus reduces the entropy penalty to the activation free energy. Dimethyl-β-CD is found to be a better catalyst for this specific reaction than β-CD because it outperforms β-CD in almost every step of catalysis. It binds Ncyclohexylmaleimide more tightly, holds both 9-anthracenemethanol and Ncyclohexylmaleimide for much longer time in its binding site, and pays smaller entropy penalty to the activation free energy of the transition state. This computational work sheds light on the mechanism of the catalytic reaction by cyclodextrins, and introduces new perspectives to the supramolecular catalysis.