An aircraft door assembly of an aircraft, having a fuselage with a door opening and a door frame, encompassing an aircraft door fittable in the door frame. The door includes a door structure having an outer skin and is liftable from a locked closed position into a unlocked closed position, pivotable into an open position located outside the door frame and outside the fuselage, pivotable from the open position back into the unlocked closed position, and lowerable into the locked closed position such that in the locked closed position, a door gap is present between the door frame and a door edge. The gap defines a space for lifting and lowering the door. The door also includes, on its outer side and on a door edge region, a door gap covering element that extends over the door gap onto the outer side of the aircraft fuselage and covers the door gap, when the door is in the locked closed position. The door gap covering element is fastened onto the door structure and is movable relative to the outer side of the outer skin.