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Neural sensing and stimulation have been the backbone of neuroscience research, brain-machine interfaces and clinical neuromodulation therapies for decades. To-date, most of the neural stimulation systems have relied on sharp metal microelectrodes with poor electrochemical properties that induce extensive damage to the tissue and significantly degrade the long-term stability of implantable systems. Here, we demonstrate a flexible cortical microelectrode array based on porous graphene, which is capable of efficient electrophysiological sensing and stimulation from the brain surface, without penetrating into the tissue. Porous graphene electrodes show superior impedance and charge injection characteristics making them ideal for high efficiency cortical sensing and stimulation. They exhibit no physical delamination or degradation even after 1 million biphasic stimulation cycles, confirming high endurance. In in vivo experiments with rodents, same array is used to sense brain activity patterns with high spatio-temporal resolution and to control leg muscles with high-precision electrical stimulation from the cortical surface. Flexible porous graphene array offers a minimally invasive but high efficiency neuromodulation scheme with potential applications in cortical mapping, brain-computer interfaces, treatment of neurological disorders, where high resolution and simultaneous recording and stimulation of neural activity are crucial.