One of the most promising applications of nanocellulose is for membranes for energy storage devices including supercapacitors, batteries, and fuel cells. Several recent studies reported the fabrication of cellulose-based membranes where ionic conductivity was confined to channels. So far, theoretical understanding of the effect of the nanoconfinement and surface charged groups on the diffusion coefficient of ions in cellulose nanochannels is missing. In the present study, we perform atomistic molecular dynamics simulations to provide this theoretical understanding and unravel mechanisms affecting the ionic diffusion in nanochannels. We demonstrate that the diffusion coefficient of ions in cellulose nanochannels is reduced in comparison to its bulk value. The change of the diffusion coefficient depends on the density of charged surface groups in nanochannels and the channel height, and it is primarily caused by the Coulomb interaction between the ions and the surface. We believe that our results reveal an important structure/property relationship in cellulose nanochannels, and they show that accounting for the dependence of the diffusion coefficient on the charge of the surface groups and channel height can be important for the Nernst-Plank-Poisson modeling of the ion conductivity in nanomembranes as well as for accurate fitting the experimental data to extract the material parameters.