A door structure for an air conditioner of a vehicle includes an indoor/outdoor air door having a dome shape. An outdoor air door has a plate shape and adjusts the amount of outdoor air introduced into the vehicle. First and second counter-flow preventing ribs are disposed vertically between the dome shaped indoor/outdoor air door and the plate shaped outdoor air door. The first counter-flow preventing rib is mounted to a first hinge which is connected to one end of the plate shaped outdoor air door. The second counter-flow preventing rib is mounted to be close to another end of the plate shaped outdoor air door. An air conditioning filter is disposed below the dome shaped indoor/outdoor air door, the plate shaped outdoor air door, and the first and second counter-flow preventing ribs and filters the introduced indoor air or outdoor air.