Pitot-type inlets are used in cruise missiles to supply air to the turbojet propulsion system. One of the main motivations for using a pitot-type inlet is to capture clear air by preventing the entry of the boundary layer into the inlet [1]. When a cruise missile with a turbojet propulsion system is launched from an aircraft, the turbojet engine cannot be used immediately because specific flight conditions must be met for the powered flight phase. Therefore, the missile glides until it reaches a certain speed. The inlet cover is designed to prevent the windmilling on the turbojet engine during the gliding phase and it is jettisoned before the engine ignition [2]. Optimizing the aerodynamic shape of the cover is crucial to minimize the gliding configuration's drag. Therefore, the gliding range can be increased. Also, it is desired for the cover to have a moment in the opening direction for safe separation. The present study focuses on the aerodynamic shape optimization of a cruise missile inlet cover. The adjoint-based optimization is conducted with the open-source SU2 software suite. The cover shape is controlled by means of a Free Form Deformation box. The design objectives are to minimize the total drag of a generic missile gliding configuration and to maximize the opening moment of the inlet cover at the same time. The software tools employed are verified against experimental data, and proper grid densities are selected. Then, optimization studies are performed for a quarter-spherical inlet cover placed over a cylindrical missile body. The cover optimization is examined with three different approaches. First, optimization is performed to minimize the drag coefficient. Second, the objective of maximizing the opening moment of the cover with respect to the hinge line is studied. Finally, a multi-objective optimization for drag minimization and moment maximization is performed. The findings are discussed in detail, and it is shown that the optimization process provides new cover shapes for increased performance in comparison to the quarter-spherical baseline cover.