The apparent shear viscosity of p-methoxybenzylidene-p'-n-butylaniline in the presence of electrohydrodynamic convection (EHC) is investigated experimentally. In the absence of an electric field, directors are almost aligned along the flow direction such that the viscosity is close to the minimum of the Miesowicz viscosities. Since EHC disturbs the flow-aligned director configuration, the viscosity increases as the applied voltage is increased in the low-voltage regime. In the high-voltage regime, however, further increasing the voltage leads to a decrease in viscosity. Microscope observations using a rheometer reveal that the decrease in viscosity occurs in the dynamic scattering mode 2 (DSM2) state, whose spatial director distribution is anisotropic due to the shear flow. By adopting the Ericksen-Leslie theory for the shear flow under the electric field, we find that the viscosity decrease can be attributed to the negative contribution of the electric stress caused by the anisotropic director distribution of the DSM2 state. DOI: 10.1103/PhysRevE.87.012501