A general multiple horizon predictive control scheme extending the Algebraic Model Predictive Control (AMPC) algorithm in its application to flight control was proposed. It was shown that by allocating prediction horizons tuned specifically to the time scales over which the outputs react, the overall response can be greatly improved. The method's ability to decouple output responses of a highly coupled longitudinal aircraft system was also demonstrated, highlighting the additional tuning capabilities that are lost when a single, global prediction horizon is used. The results demonstrate the AMPC algorithms ability in controlling multiple outputs of the linear, longitudinal aircraft model. The performance of the algorithm will be assessed by analyzing the aircraft's response in tracking a commanded climb rate while regulating forward airspeed.