A theoretical framework to increase the sensitivity of graphene-based surface plasmon resonance (SPR) biosensors by the application of electrical bias voltage across the sensor surface is presented. Graphene layers deposited on thin gold film (50 nm) form the sensor surface system where the surface plasmon is excited. The real and imaginary parts of the refractive index of this gold-graphene system can be controlled by tuning its chemical potential using electrical modulation. Numerical calculations show a promising method to enhance the sensitivity of graphene-based SPR biosensors.