The wettability of graphene on various substrates has been intensively investigated for practical applications including surgical and medical tools, textiles, water harvesting, self-cleaning, oil spill removal and microfluidic devices. However, most previous studies have been limited to investigating the intrinsic and passive wettability of graphene and graphene hybrid composites. Here, we report the electrowetting of graphene-coated metal meshes for use as electroactive flow control devices, utilizing two antagonistic functions, hydrophobic repellency versus liquid permeability. Graphene coating was able to prevent the thermal oxidation and corrosion problems that plague unprotected metal meshes, while also maintaining its hydrophobicity. The shapes of liquid droplets and the degree of water penetration through the graphene-coated meshes were controlled by electrical stimuli based on the functional control of hydrophobic repellency and liquid permeability. Furthermore, using the graphene-coated metal meshes, we developed two active flow devices demonstrating the dynamic locomotion of water droplets and electroactive flow switching.