The electrical control of photonic crystal (PhC) lasers has been an attractive but challenging issue. Laser operation by electrical injection is of key importance for the viability and applicability of the PhC lasers. Another key factor is the electrical modulation of the laser output. The Fermi level of a graphene monolayer can be controlled by electrical gating, which adjusts its optical absorption. In this study, a graphene monolayer sheet is integrated on top of a two-dimensional PhC structure composed of InGaAsP multiple-quantum-wells (MQWs) in order to demonstrate the electrical modulation of a high-power (microwatt-scale) PhC band-edge laser. The introduced dielectric spacer layer presets the delicate balance between the optical gain from the MQWs and optical loss at the graphene monolayer. The proposed device is covered by an ion-gel film, which enables a low-voltage laser modulation at |Vg|≤1 V. The modulation is extensively investigated experimentally, and the obtained results are confirmed by performing numerical simulations.