Boron nitride nanotubes (BNNTs) have been shown to possess many excellent physical properties, including thermal and mechanical properties. In this work, we report on superior water permeation properties of BNNTs. Specifically, using molecular dynamics simulations, we found that water molecules permeate through the (5,5) boron nitride nanotube, while a (5,5) carbon nanotube (CNT) of approximately the same diameter does not conduct water. The relatively strong interactions between the nitride atoms of the BNNT and water molecules play a key role in the continuous wetting behavior of the BNNT. The properties of water, such as the axial diffusion coefficient and the hydrogen bonding, inside the (5,5) BNNT were found to be comparable to those inside the (6,6) CNT, even though the diameter of the (5,5) BNNT is about 1.3 A smaller than that of the (6,6) CNT.