There is the connexon between neighboring cells in human bodies, which normally has the cylindrical channels with the diameter about 1.5nm. The analysis is here derived for the water transport through such a narrow channel based on the nanoscale flow equation by considering the dynamic, interfacial slippage and non-continuum effects of the water. The calculation shows that when the intracellular fluids of the neighboring cells are not obviously different, there is no wall slippage in the connexon channel and the water flow rate through the channel is significantly smaller than that calculated from the classical Hagen-Poiseuille equation due to the viscous and non-continuum effects of the water; However, when the intracellular fluids of the neighboring cells are much different, there would be the intracellular pressure difference between the neighboring cells which is large enough for starting the wall slippage in the channel; For the wall slippage case, the water transport rate through the channel is normally much greater than and can be 1 to 7 orders larger than the classical equation calculation, just only by the power losses ranging between 1.0E-14Watt and 1.0E-9Watt on each channel. This transport characteristic is very important for quickly achieving the balance between the neighboring cells by fast transporting the water and other small substances through the connexon channel.