Nanotube membranes show exceptional transport properties for water and other substances, which can be utilized in many attractive applications, such as molecular sieving, drug delivery, and water purification. To design effective nanotube membranes for these applications, it is necessary to understand the transport properties of water confined in nanotubes. The diffusion of water inside nanotubes plays an important role in this process. By performing extensive molecular dynamics simulations, we investigate the effects of temperature and pore size on water diffusion inside carbon nanotubes. The results demonstrate that the temperature dependence of self-diffusion coefficient of water inside carbon nanotubes is obviously different for various pore sizes. It can be found that for nanotube with diameter of 0.681 nm and 0.820–0.905 nm, the self-diffusion coefficient decreases remarkably with the decreasing temperature due to the change of water structure, which is not obvious for water in nanotubes with other pore sizes. This fundamental study attempts to provide deep insights in understanding the transport process across nanotube membranes.