This paper presents a method for active vibration control of smart thin cantilever plates. For model formulation needed for controller design and simulations, finite difference technique is used on the cantilever plate response calculations. Piezoelectric patches are used on the plate, for which a neural network based control algorithm is formed and a neurocontroller is produced to calculate the required voltage to be applied on the actuator patch. The neurocontroller is trained and run with a Kalman Filter for controlling the structural response. The neurocontroller performance is assessed by comparing the controlled and uncontrolled structural responses when the plate is subjected to various excitations. It is shown that the acceleration response of the cantilever plate is suppressed considerably validating the efficacy of the neurocontroller and the success of the proposed methodology.