Artificial gas-lift (AGL) process is one of the techniques used in the oil industry to maintain the oil flow from the well to the production line when the reservoir pressure drops. Controller design for such a system is very challenging as it exhibits highly nonlinear dynamics. In this work, the predictive generalized minimum variance control (PGMVC) is employed to derive a robust controller for artificial gas-lift process (AGL). A closed-form optimal control law is obtained based on Taylor series approximation. Moreover, a nonlinear disturbance observer is combined with the controller to ensure zero-steady state error under model uncertainty and external disturbance. The composite controller is applied to stabilize casing-heading instability occurring in wells. Through simulation studies, the effectiveness of the proposed controller is demonstrated.