I am planning to travel to Iran (I am Iranian also) from the U.S. (and I have a permanent residency card i.e. Green card holder) ... do I need a transit visa at Vienna airport?
Short Answer: No, you don't need a transit visa for Austria.
Long Answer: If an airline passenger is refused entry at a transit point or destination, the airline is required to return the passenger to the point of departure at the airline's expense (although they may try to recover the cost from the passenger). Thus, airlines are very careful to determine what documents are required by a particular passenger's travel before allowing that passenger to board. Airlines use the IATA database Timatic to reveal what documents are required.
Putting your information into Timatic through this online portal (there other others), generates this:
National Iran (IR)
/Residence USA (US)
Transit Austria (AT)
/Destination Iran (IR)
ALSO CHECK DESTINATION INFORMATION BELOW
TWOV (Transit Without Visa): Visa required, except for Nationals of Iran, arriving from a non-Schengen Member State with a confirmed onward ticket for a flight to a third country which is not a Schengen Member State. They must:
- have a residence permit issued by USA, and
- stay in the international transit area of the airport, and
- have documents required for the next destination.
Passport required. - Nationals of Iran are allowed to enter with an expired passport
VISA NOT REQUIRED.
Thus, because you will arrive from a non-Schengen state with an onward ticket for a third country which is not a Schengen state, you can transit in Vienna without a transit visa provided you stay in the airport's international transit area.