The dynamics of water molecules confined in MCM-41 was investigated by quasi-elastic neutron scattering. The measurement was performed for three water-filled MCM-41 samples with different pore sizes in the temperature range 200-300 K. The spectra were analyzed by using a model employed by Teixeria et al. in a study for hulk water. This model is composed of two motions of water molecules: rotational and translational diffusions. For the translational diffusion, water molecules in MCM-41 are, on the whole, less mobile than those in bulk water, and the mobility is decreased by narrowing of the pore size. The residence time of translational diffusion of the confined water molecules shows the Arrhenius type of temperature dependence, which is in contrast to a non-Arrhenius behavior for bulk water. This implies that a growth of the hydrogen-bond network of water is hindered in a confined space by surface field. Spectra of MCM-41 sample having monolayer water were also measured and could be analyzed with a model in which only rotational diffusion is an allowed motion of the monolayer water molecules.