Electric Ducted Fans (EDF) provide several advantages over conventional propellers. In hover they can provide additional thrust for the same power and rotor diameter meaning smaller footprint of the aircraft on the take-off/landing area. In axial flight the shroud reduces the tip losses of the rotor especially in higher flight speeds. Unfortunately, due to the difference in velocity streamlines in both flight regimes, a shroud optimized for hover will have negative effects on the propulsion efficiency in axial flight. This means that a compromise must be made in the design of a propulsion system intended for fixed wing Vertical Take-off Landing (VTOL) aircraft with efficient axial flight capabilities for example, using separate systems for hover and for axial flight. Here, an optimization methodology is proposed for a novel design of a morphing ducted fan. Firstly, the optimal geometry for hover was obtained by genetic algorithm (GA) optimization. After that, GA optimization was used to obtain the optimal geometry for cruise with the introduction of constraints as to be able to create a geometry capable of morphing. In the end, the internal structure of the duct which can provide accurate control of the inlet and outlet was defined by utilizing techniques similar to the ones used in morphing wing designs.