We report the realization of magnetoelectric switching of the perpendicular exchange bias in Pt/Co/α-Cr2O3/Pt stacked films. The perpendicular exchange bias was switched isothermally by the simultaneous application of magnetic and electric fields. The threshold electric field required to switch the perpendicular exchange bias was found to be inversely proportional to the magnetic field, which confirmed the magnetoelectric mechanism of the process. The observed temperature dependence of the threshold electric field suggested that the energy barrier of the antiferromagnetic spin reversal was significantly lower than that assuming the coherent rotation. Pulse voltage measurements indicated that the antiferromagnetic domain propagation dominates the switching process. These results suggest an analogy of the electric-field-induced magnetization with a simple ferromagnet.