Water confined within nanoscale geometries under external field has many interesting properties which is very important for its application in biological processes and engineering. Using molecular dynamics simulations, we investigate the effect of external fields on polarization and structure as well as phase transformations of water confined within carbon nanotubes. We find that dipoles of water molecules tend to align along external field in nanoscale cylindrical confinement. Such alignment directly leads to the longitudinal electrostriction and cross-sectional dilation of water in nanotube. It also influences the stability of ice structures. As the electrostatic field strengthens, the confined water undergoes phase transitions from a prism structure to a helical one to a single chain as the electrostatic field strengthens. These results imply a rich phase diagram of the confined water due to the presence of external electriostatic field, which can be of importance for the industrial applications in nanopores.