Dynamics of water and methylcellulose (MC) molecules in MC aqueous solution has been studied by means of quasi-elastic neutron-scattering (QENS) measurements. The dynamic structure factor S(Q,E) of the MC aqueous solution was fitted well to the sum of Lorentzian and delta functions. The former is attributed to diffusive motion of water molecules and the latter to local vibrational motion of MC molecules. The self-diffusion coefficient of water molecules was obtained from the Q dependence of the half-width at half-maximum (HWHM) of the Lorentzian function, while the mean-square displacement of MC molecules from the Q dependence of the intensity of the delta term. Both the diffusion coefficient and the mean-square displacement gradually increased on heating and abruptly decreased around the thermal gelation temperature (around 320 K). The present results revealed that the microscopic motions of both water and MC molecules give rise to dynamic slowing down on thermal gelation.