Due to their facile manipulation and transport property, carbon nanotubes (CNTs) are the best candidate for ions and water channels with high selectivity behaviors. In this work, water permeability and salt rejection in the water nanochannel made of CNT(12,12), CNT(13,13) and CNT(14,14) encapsulating fullerene were investigated with or without applying various hydrostatic pressures using molecular dynamics (MD) simulation. In addition to high water permeation, the water nanochannel reduced ion permeation. Based on the results, salt rejection in the channels made of CNT(12.12) and CNT(13.13) encapsulating fullerene was acquired 100%. In the water nanochannel made of CNT(14,14) encapsulating fullerene, a significant water permeability was achieved about 16.22 +/- 0.85 x 10(-13) cm(3).s(-1) which is more than the water permeability was reported for the natural water channels and a remarkable salt rejection (similar to 91.62%) was obtained under 5 MPa hydrostatic pressure. It is elucidated that the value of water permeability in this channel was approximately doubled by increasing the hydrostatic pressure. Water and ion permeation, interaction energy of the fullerene with the carbon nanotube surface and the free energy profile for water molecules through the highly selective nanochannels were assessed. In order to study the operation of the water nanochannels, the movement pattern of the fullerene inside the CNT as well as the forces applied to the fullerene was investigated. The motion of the fullerene inside carbon nanotubes was affected by the exerted forces from water molecules on the fullerene and the interaction energy between CNT wall and fullerene. Therefore stronger interaction between fullerene and CNT wall prevents fullerene exiting the nanochannel. The CNT(14,14) encapsulating fullerene shows less energy barrier when water molecules cross the fullerene inside the nanochannel. The aforementioned results demonstrated that carbon nanotube encapsulating fullerene is a high-performance candidate water nanochannel with selective behavior to water molecules and tremendous salt rejection.