The transport properties, including the diffusivity and viscosity, of water confined in hydrophobic nanopores and nanoslits were studied by molecular dynamics simulations. The results show that the diffusion coefficient in nanopores and nanoslits is markedly lower than that in the bulk. But the viscosity is much larger than that in bulk. The parallel diffusion coefficient is obviously larger than the perpendicular ones. The diffusion coefficient in the channel pore is ever less than that in the slit pore at the same pore width, but the viscosity is larger. The temperature and density affect significantly the diffusivity and viscosity in nanopores and nanoslits. Lower density water exhibits some special characteristics on density profiles in nanopores and nanoslits at lower temperatures, and the density profiles show a change from homogeneous to inhomogeneous as the pore width is reduced. Even clusters occurred in micropores.