The video showed an aerial view of an airport and a city, said to be Kandahar in Afghanistan.
Tehran has long claimed it managed to reverse-engineer the RQ-170 Sentinel and that it is capable of launching its own production line for the unmanned aircraft.
The TV also showed images purported to be the Sentinel landing at a base in eastern Iran.
The Revolutionary Guard's air space chief, General Amir Ali Hajizadeh, says in another part of the video that only after it captured the drone did Iran realise it "belongs to the CIA".
Iran claims it "took control of the drone and landed it" but US officials have said it malfunctioned and had to land.