In this paper, an augmented predictive functional control approach is investigated to design a missile autopilot system, which can be expressed as a linear model with state-dependent coefficient matrices. A novel performance index depending on the reference trajectory, the output prediction and the set-point is proposed to improve the closed-loop dynamic performance. An augmented predictive functional control strategy is designed based on the proposed index and the stability is proven by using the Z-transform. In order to demonstrate the performance of the proposed approach, numerical simulations comparing the predictive functional control in the missile autopilot system are performed. Finally, results from comprehensive simulations are presented to evaluate the proposed approach in the presence of input constraints and abrupt disturbances.