The giant electrorheological (ER) fluid is based on the principle of a polar molecule dominated electrorheological (PM-ER) effect. The response of the shear stress for PM-ER fluid in alteate electric fields with triangle/square wave forms for different frequencies has been studied. The results show that the shear stress cannot well follow the rapid change of electric field and the average shear stresses of PM-ER fluids decrease with the increasing frequency of the applied field due to the response decay of the shear stress on applied field. The behavior is quite different from that of traditional ER fluids. However, the average shear stress of PM-ER fluid in a square wave electric field of ±E at low frequency can keep at high value. The obtained knowledge must be helpful for the design and operation of PM-ER fluids in the applications.