Rheological properties of water films nanoconfined in two parallel Au plates are investigated with the aid of molecular dynamics simulations. The density distribution, velocity profile, and diffusion coefficients of the water film in a Couette flow are studied. Shear viscosity and its dependence on the shear rate of the water film are also examined in the present research. It is found that the density of the water molecules near the plates is much higher than that in the other regions. This indicates that many water molecules are adsorbed by the plates and adsorbed layers are formed in the vicinity of the plates. The diffusion of the whole film increases dramatically as the shear rate becomes greater than 1010 s-1. The shear viscosity decreases as the shear rate increases, especially for the water film with a small thickness, which indicates the shear-thinning behavior for viscosity of the nanoconfined film. Moreover, an increase in shear viscosity with a decrease in the film thickness can also be found in the present study.