Since its first discovery in 2004, graphene has been found to host a plethora of unusual electronic transport phenomena, making it a fascinating system for fundamental studies in condensed matter physics as well as offering tremendous opportunities for future electronic and sensing devices. Typically, electronic transport in graphene has been investigated via resistivity measurements; however, these measurements are generally blind to spatial information critical to observing and studying landmark transport phenomena in real space and in realistic imperfect devices. We apply quantum imaging to the problem and demonstrate noninvasive, high-resolution imaging of current flow in monolayer graphene structures. Our method uses an engineered array of near-surface, atomic-sized quantum sensors in diamond to map the vector magnetic field and reconstruct the vector current density over graphene geometries of varying complexity, from monoribbons to junctions, with spatial resolution at the diffraction limit and a projected sensitivity to currents as small as 1 μA. The measured current maps reveal strong spatial variations corresponding to physical defects at the submicrometer scale. The demonstrated method opens up an important new avenue to investigate fundamental electronic and spin transport in graphene structures and devices and, more generally, in emerging two-dimensional materials and thin-film systems.