Diffusion dynamics of guest molecules in nanopores has been studied intensively because diffusion is center on a number of research fields such as separation, drug delivery, chemical reactions, and sensing. In the present work, we report an experimental investigation of the self-diffusion of water inside carbon nanotube (CNT) channels using a pulsed field gradient (PFG) NMR method. The dispersion of CNTs homogeneously in water and cooling to temperatures below the melting point of bulk water allow us to probe the translational motion of confined water molecules. The results demonstrate that the self-diffusion coefficient of water in CNTs is highly dependent on the diffusion time and CNT diameter. In particular, the diffusivity of water in double-walled carbon nanotubes (DWNTs) with an average inner diameter of 2.3 +/- 0.3 nm is twice that in multiwalled carbon nanotubes (MWNTs) with an average inner diameter of 6.7 +/- 0.8 nm in the temperature range of 263-223 K. In addition, the effective self-diffusion coefficient in DWNTs is 1 order of magnitude higher than that reported for mesoporous silica materials with a similar pore size. The faster diffusivity of water in CNTs could be attributed to the ordered hydrogen bonds formed between water molecules within the confined channels of CNTs and the weak interaction between water and the CNT walls.