Exploring new reverse osmosis (RO) membranes that break the permeability-selectivity trade-off rule is the ultimate goal in seawater desalination. Both nanoporous monolayer graphene (NPG) and carbon nanotube (CNT) channels have been proposed to be promising candidates for this purpose. From the perspective of membrane thickness, both NPG and CNT can be classified into the same category, as NPG is equivalent to the thinnest CNT. While NPG has the advantage of a high water flux rate and CNT is excellent at salt rejection performance, a transition is expected in practical devices when the channel thickness increases from NPG to infinite-sized CNTs. By employing molecular dynamics (MD) simulations, we find that as the thickness of CNT increases, the water flux diminishes but the ion rejection rate increases. These transitions lead to optimal desalination performance around the cross-over size. Further molecular analysis reveals that this thickness effect originates from the formation of two hydration shells and their competition with the ordered water chain structure. With the increase in CNT thickness, the competition-dominated ion path through CNT is further narrowed. Once above this cross-over size, the highly confined ion path remains unchanged. Thus, the number of reduced water molecules also tends to stabilize, which explains the saturation of the salt rejection rate with the increasing CNT thickness. Our results offer insights into the molecular mechanisms of the thickness-dependent desalination performance in a one-dimensional nanochannel, which can provide useful guidance for the future design and optimization of new desalination membranes.