Memristors with rich interior dynamics of ion migration are promising for mimicking various biological synaptic functions in neuromorphic hardware systems. A graphene-based memristor shows an extremely low energy consumption of less than a femtojoule per spike, by taking advantage of weak surface van der Waals interaction of graphene. The device also shows an intriguing programmable metaplasticity property in which the synaptic plasticity depends on the history of the stimuli and yet allows rapid reconfiguration via an immediate stimulus. This graphene-based memristor could be a promising building block toward designing highly versatile and extremely energy efficient neuromorphic computing systems.