Methanediol is a product of the hydration of formaldehyde and is more abundant than formaldehyde in aqueous solution. We carried out a number of quantum chemical simulations to study the decomposition of methanediol in aqueous solution. The decomposition of a methanediol proceeds by transferring a proton from a hydroxyl to an oxygen atom of the other hydroxyl in the methanediol. The decomposition of the methanediol completes after the cleavage of the bond between the formaldehyde and the water molecule. The probability of the proton transfer increases by the quantum mechanical tunneling at the low temperature because the width of the potential barrier for the decomposition becomes similar to the de Broglie wavelength of the proton. We consider the catalytic effect of water molecules in aqueous solution. The structure of the methanediol is not required to change significantly when undergoing decomposition due to the active role of water molecules to transfer a proton. We consider three types of arrangement for water molecules with respect to a methanediol: (1) a ring structure formed by a methanediol and water molecules; (2) a water cluster attracted to a methanediol by hydrogen bonds; and (3) a water cluster and additional water molecules, both of which are attracted to a methanediol by hydrogen bonds. The activation energy for the decomposition is reduced by a water cluster more efficiently than water molecules in a ring structure. However, the activation energy reduced by a water cluster is still larger than that obtained from laboratory experiments. We include water molecules that are attracted to a methanediol by hydrogen bonds during the water-cluster-catalyzed decomposition of a methanediol. The hydrogen bonds with the water molecules permit little change in the structure of the methanediol during the decomposition and play a significant role to reduce the activation energy for the decomposition. The rate constant obtained from the theoretical simulation agrees well with that determined by the laboratory experiment.