Graphene nanostructures are proposed as promising materials for nanoelectronics such as transistors, sensors, spin valves and photoelectric devices. Zigzag edge graphene nanostructures had attracted broad attention due to their unique electronic properties. Anisotropic hydrogen-plasma etching has been demonstrated as an efficient top-down fabrication technique for zigzag-edged graphene nanostructures with a sub-10 nm spacial resolution. This anisotropic etching works for monolayer, bilayer and multilayer graphene and the etching rate depends on substrate temperature with a maximum etching rate at arround 400 C. It has been also founded that the anisotropic etching is also affected by the surface roughness and charge impurities of the substrate. Atomically flat substrates with no charge impurities would be ideal for the anisotropic etching. So far the understanding of hydrogen-plasma anisotropic etching, e.g. whether hydrogen radicals or hydrogen ions dominate the etching process, remains unclear. In this work, we investigated the anisotropic etching of graphene under electrical field modulations. Bilayer graphene peeled off from grahpite on SiO2 substrate was used as the experimental object. 2 nm-Ti (adhesive layer) and 40 nm-Au electrodes was deposited by electronic beam evaporation for electrical contacts. Gate voltates were applied to the bilayer graphene samples to make them either positively or negitively charged. These charged samples were then subjected to the hydrogen anisotropic etching at 400 C under the plasma power of 60 W and gas pressure of 0.3 Torr. The etching rates were characterized by the sizes of the etched hexagonal holes. We found that the etching rate for bilayer graphene on SiO2 substrate depends strongly on the gate voltages applied. With gate voltages sweeping from the negative to the positive, etching rate shows obvious decrease. 45 times of etching rate decrease was seen when sweeping the gate voltages from -30 V (positively charged) to 30 V (negatively charged). This gate-dependent anisotropic etching suggests that hydrogen ions rather than radicals plays a key role during the anisotropic etching process since the negatively charged graphene could neutralize the hydrogen ions quickly thus make them unreactive. The present work provides a strategy for fabrication of graphene nanostructures by anisotropic etching with a controllable manner.