Quasielastic neutron scattering (QENS) spectra of water-filled MCM-41 samples (pore diameters: 21.4 and 28.4 Angstrom) were measured over the temperature range 238-298 K and the momentum transfer range 0.31-0.99 A(-1) to investigate the dynamics of confined water molecules. The spectra, which consist mainly of contributions from the translational diffusion of water molecules, were analyzed by using the Lorentzian and the stretched exponential functions. Comparison of the fits indicated that the latter analysis is more reliable than the former one. The fraction of immobile water molecules located in the vicinity of the pore walls, which give an elastic component, was found to be 0.044-0.061 in both pores. The stretch exponent beta was determined as 0.66-0.80. It was shown that the translational diffusion of water molecules in the pores is decelerated by confinement and that the deceleration becomes marked with a decrease in pore size. The ratios of the translational diffusion coefficient D(T) of confined water to that of bulk water at room temperature were within a range of 0.47-0.63.