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We report on a systematic study of bias-voltage-induced modulation of magnetic and electronic properties of bilayer zigzag graphene nanoribbons (Z-GNRs) on Si(001) substrate by first-principles calculations. We show that the intrinsically nonmagnetic bilayer Z-GNRs exhibit magnetic ordering on the top layer while the bottom layer serves as a nonmagnetic buffer layer when adsorbed on the substrate. Interestingly, the adsorbed bilayers display distinct ribbon-width-dependent magnetoelectric effect under bias voltages. The magnetoelectric coefficient oscillates with increasing ribbon width, which arises from an interesting interplay of the interaction of the bottom ribbon layer with the substrates and the decay length of the localized edge states in Z-GNRs. Moreover, our calculations reveal that the electronic band gap of the top ribbon layer also can be effectively modulated by the applied bias voltage, which can lead to a semiconductor-to-metal transition in the top magnetic semiconductor layer. These results provide insights into the intriguing behaviors of Z-GNRs on substrates and raise the prospects of developing an innovative path toward graphene-based electronic and spintronic devices by integrating the emerging nanoscale graphene systems with existing silicon technology.