A neuro-memristive circuit that impersonates the synaptic plasticity of a biological synapse is proposed in this literature. The proposed memristive circuit effectively operates within the frequency bands of brainwaves and exhibits the similar plasticity attributes of brain states corresponding to these wave bands. Specifically, it efficiently imitates the short-term and long-term plasticity phenomena of a synapse. In addition, it exhibits the distinct bio-realistic attributes (i.e. strong stimulation, exponentially decaying conductance trace of synapse, and voltage dependent synaptic responses) of a neuron. The neuro-memristive circuit is designed in SPICE and the bio-realistic functionalities are demonstrated via various simulations.