The viscosity of a one-component polarizable fluid in an electric field is studied by computer simulations. The fluid viscosity increases with the field through three stages. In a weak field, the fluid remains Newtonian, although its viscosity increases. At this stage, while drifting in the how direction, particles diffuse in the direction perpendicular to the how. In an intermediate electric field, the fluid has tilted and broken chains moving with the flow and the fluid becomes non-Newtonian. The viscosity eta and the shear rate gamma over dot have the relationship eta=eta(0)e(-gamma over dot tau), where tau is the relaxation time and eta(0) is exponentially proportional to the dipolar interaction energy and the volume fraction. Ina strong electric field, the fluid contains condensed chains that provide yield stress and hysteresis.