Diffusion of water confined in natural bentonite clay is studied using the quasi-elastic neutron scattering (QENS) technique. X-ray diffraction shows a well-defined crystalline structure of the clay with an interlayer spacing of 13 Angstrom. The QENS experiment has been carried out on hydrated as well as dehydrated clay at 300 K. Significant quasi-elastic broadening was observed in case of hydrated bentonite clay whereas dehydrated clay did not show any broadening over the instrument resolution. Analysis of QENS data reveals that diffusion of water occurs through jump diffusion characterized by random distribution of jump lengths. Diffusion of water in clay is found to be hindered vis a vis bulk water.