The problem of maintenance scheduling and staffing at an aircraft heavy maintenance service company is studied. The objective is to establish an integrated aircraft maintenance schedule and maintenance technicians’ rosters to fulfil different maintenance requests while minimizing the overall tardiness cost and labor cost. Upon receiving the maintenance requests, the hangar planner has to determine if the maintenance company is capable to serve the aircraft within the planning period, then allocate the parking stands and staying time of each aircraft in the hangar for the subsequent maintenance operations. Due to the complexity of the combinatorial problem, the commercial solver using branch-and-bound algorithm is incapable to tackle with the medium-sized instance within reasonable time. To enhance the computational efficiency, a framework of branch-and-cut algorithm is proposed in this paper, aiming to decompose the original model and tighten the lower bound of the original problem by the effective cuts. The concept of combinatorial benders’ decomposition algorithm is adopted in the development of algorithm.