Memristive neuromorphic systems represent one of the most promising technologies to overcome the current challenges faced by conventional computer systems. They have recently been proposed for a wide variety of applications, such as non-volatile computer memory, neuroprosthetics, and brain-machine interfaces. However, due to their intrinsically nonlinear characteristics, they present a very complex dynamic behavior, including self-sustained oscillations, seizure-like events and chaos, which may compromise their use in closed-loop systems. In this work, a novel intelligent controller is proposed to suppress seizure-like events in a memristive circuit based on the Hodgkin-Huxley equations. For this purpose, an adaptive neural network is adopted within a Lyapunov-based nonlinear control scheme to attenuate bursting dynamics in the circuit, while compensating for modeling uncertainties and external disturbances. The boundedness and convergence properties of the proposed control scheme are rigorously proved by means of a Lyapunov-like stability analysis. The obtained results confirm the effectiveness of the proposed intelligent controller, presenting a much improved performance when compared to a conventional nonlinear control scheme.