The official IRNA news agency says the Falcon 20, which belonged to the State Aviation Organization, was on a test flight when it crashed late on Monday off Kish Island, a well-known tourist resort.
The agency says all four bodies were recovered and the crash is being investigated. Earlier, IRNA reported there were five on board but later corrected the number.
Iran has had a history of air accidents, often blamed on poorly maintained planes.
The latest major crash was in Jan. 2011, when a passenger plane broke to pieces on impact while trying an emergency landing in a snowstorm in northwestern Iran, killing at least 77 people.