Graphene has enormous potential as a solid lubricant at sliding electrical contact interfaces of micro-/nanoelectromechanical systems that suffer severe wear. Understanding the velocity-dependent friction of graphene under different applied voltages contributes to the application of graphene in sliding electrical contact scenarios. The friction of graphene, measured by conductive atomic force microscopy, under low applied voltage increases logarithmically with sliding velocity─the same as when no voltage is applied but at a faster rate of increase. The variation of friction was explained by the thermally activated Prandtl-Tomlinson model with increased potential barrier and temperature because of the applied voltage. An opposite trend in which friction decreases with sliding velocity is observed under high applied voltage. Topography, adhesion measurements, and SEM characterization demonstrate the wear of the tip. Moreover, the tip wears more severely at low sliding velocity compared to a high sliding velocity. It was interpreted that the excessive Joule heat at the electrical contact interface under high applied voltage weakens the mechanical properties of the tip, resulting in wear and high friction. The increase in the sliding velocity could accelerate the Joule heat transfer and reduce wear and friction. The studies provide beneficial guidelines for the design of graphene-lubricated sliding electrical contact interfaces.