The competition in the airline industry has rapidly increased during the last decades, especially with the entrance in the market of low-cost carriers. The high costs incurred in Maintenance, Repair and Overhaul (MRO) activities are generating a great interest in the improvement of maintenance operations as a way to stay competitive in the market. At the same time, the new generations of aircraft are increasingly being equipped with sensors that monitor the component's health condition. This stimulates the shift towards data-driven predictive aircraft maintenance, which is enabled by prognostics. This study proposes a model for maintenance scheduling of a fleet of aircraft based on component Remaining-Useful-Life prognostics and a limited stock of available spares. A discrete-time, rolling horizon approach is proposed, resulting in a sequence of scheduling time windows. For each time window, the goal is to find an optimal maintenance schedule. Moreover, the scheduling model considers three stages in decreasing order of maintenance priority, from critical aircraft leading to grounded condition, to predictive alerts, to non-critical failures. The results show that a cost-efficient maintenance schedule for a large fleet of aircraft is generated with an outstanding computational performance. Moreover, the aircraft operating costs are significantly reduced in the long-run, even when considering limited spares.