Aircraft's availability is certainly one of the most important features of modern avionic industry. The aircraft maintenance scheduling is one of the major decisions an airline has to make during its operation. When an aircraft maintenance event occurs, the overhaul tasks management process requires the execution of all tasks to perform and has to guarantee the on-time aircraft delivery and the respect of the daily flight schedule. Though maintenance scheduling comes as an end stage in an airline operation, it has potential for cost savings. Maintenance scheduling is an easily understood but difficult to solve problem. Given a flight schedule with aircraft assigned to it, the aircraft maintenance-scheduling problem is to determine which aircraft should fly which segment and when and where each aircraft should undergo different levels of maintenance check. The objective of this paper is to minimize the aircraft maintenance planning time and to show how to create a plan with critical path analyses under fuzzy environment. We use trapezoidal fuzzy numbers for activity times and Activity-on-Node (AON) representation in fuzzy critical path method (FCPM). An illustrative example is given for Aircraft Gas Turbine Engine Repair/Overhaul problem.