Graphene has shown the great potential applications in the field of solid lubricants due to its outstanding mechanical properties and chemical inertness. The introduction of interfacial current at the graphene-lubricated surface is expected to tune the lubrication performance of graphene. Here in this work, an atomistic configuration of single-crystal silicon tip sliding against graphene supported by an elastic substrate is constructed to investigate the current-carrying friction behavior of graphene by using molecular dynamics simulations. The effects of applied voltages, normal loads and substrate stiffnesses on the current-carrying friction behavior of graphene are systematically explored. The simulation results show that when the bias voltage is applied to the graphene-based system, the friction force undertaken by the tip is one order of magnitude larger than when applying no bias voltage. The friction increases with the magnitude of bias voltage increasing, but the increasing rate varies in different directions of bias voltage. A similar friction-voltage relationship of graphene under different normal loads and substrate stiffnesses indicates its relatively stable current-carrying friction behavior and the robust current-carrying effect. The increased friction force of graphene after the introduction of interfacial current can be attributed to the expansion of current-carrying region, causing Coulomb interactions instead of van der Waals interactions to dominate the adhesions at the friction interface. Based on the Prandtl-Tomlinson model, the current-carrying friction mechanism of graphene is systematically discussed. It is found that such a friction mechanism is different from the pucker effect of graphene, but follows the energy barrier theory. This work promotes the graphene to be used as the typical solid lubricant under the complex operation conditions with the voltage-induced current going through friction interfaces.