The viscosity of water under an external electric field of 0.00-0.90 V/nm was studied using both molecular dynamics simulations and atomistic modeling accounting for intermolecular potentials. For all temperatures investigated, the water viscosity becomes anisotropic under an electric field: the viscosity component parallel to the field increases monotonically with the field strength, E, while the viscosity perpendicular to the field first decreases and then increases with E. This anisotropy is believed to be mainly caused by the redistribution of hydrogen bonds under the electric field. The preferred orientation of hydrogen bonds along the field direction leads to an increase of the energy barrier of a water molecule to its neighboring site, and hence increases the viscosity in that direction. However, the probability of hydrogen bonds perpendicular to the electric field decreases with E, together with the increase of the average number of hydrogen bonds per molecule, causing the perpendicular component of water viscosity to first decrease and then increase with the electric field.