The viscosity of the binary fluid can be changed drastically by imposing an external electric field. We investigate the relation between the structure of domains and the change of viscosity by performing simulations of the system composed of two kinds of fluids inserted between two plates of electrodes. It is found that the stress is significantly increased under applied electric fields as compared with the one of system under no external field. The initially dispersed domains are strongly deformed and bridge between two electrodes under electric fields. Under shear flows we also find that the elongated domains are broken up at slip regions. ©2000 American Institute of Physics.