The plane, an Airbus A300B2, registered as EP-IBU and flown by Captain Mohsen Rezaian, a veteran pilot with 7,000 hours of flight time, left Bandar Abbas at 10:17 am Iran time (UTC +03:30), 27 minutes after its scheduled departure time. It should have been a 28-minute flight. After takeoff, it was directed by the Bandar Abbas tower to turn on its transponder and proceed over the Persian Gulf. The flight was assigned routinely to commercial air corridor Amber 59, a twenty-mile (32 km)-wide lane on a direct line to Dubai airport. The short distance made for a simple flight pattern: climb to 14,000 feet (4,300 m), cruise for a short time, and descend into Dubai. The airliner was transmitting the correct transponder "squawk" code typical of a civilian aircraft and maintained English-speaking radio contact with appropriate air traffic control facilities.

On the morning of 3 July, the Vincennes was passing through the Strait of Hormuz returning from an escort duty. A helicopter from the USS Vincennes received small arms fire from Iranian patrol vessels, as it observed from high altitude. The Vincennes moved to engage the Iranian vessels, in the course of which they all violated Omani waters and left after being challenged and ordered to leave by a Royal Navy of Oman warship. The Vincennes then pursued the Iranian gunboats, entering Iranian territorial waters to open fire. The USS Sides and USS Elmer Montgomery were nearby. Thus, the USS Vincennes was in Iranian territorial waters at the time of the incident, as admitted by the US government in legal briefs and publicly by Admiral William Crowe on Nightline. Admiral Crowe denied a U.S. government coverup of the incident and claimed that the USS Vincennes's helicopter was in international waters initially, when it was first fired upon by the Iranian gunboats.
Contrary to the accounts of various USS Vincennes crewmembers, the Iranian airliner was climbing at the time and its radio transmitter was "squawking" on the Mode III civilian code only rather than on military Mode II, as recorded by the USS Vincennes' shipboard Aegis Combat System.
After receiving no response to multiple radio challenges, the USS Vincennes fired two surface-to-air missiles at the airliner. One of the missiles hit the airliner, which exploded and fell in fragments into the water. Everyone on board was killed.
Of course a coverup took place and the official position of the US Government was that theVincennes mistakenly identified the Iranian airliner as an attacking military fighter. However as mentioned above all evidence points otherwise and it was to later come out that the Captain was a loose cannon:
The destruction of the aircraft "marked the horrifying climax to Captain Rogers' aggressiveness, first seen four weeks ago."His comment referred to incidents on 2 June, when Rogers had sailed the Vincennes too close to an Iranian frigate undertaking a lawful search of a bulk carrier, launched a helicopter within 2–3 miles (3.2–4.8 km) of an Iranian small craft despite rules of engagement requiring a four-mile (6.4 km) separation, and opened fire on small Iranian military boats.
Iran did not buy the 'fighter jet' excuse:
Even if the aircraft had been an Iranian F-14, Iran argued, the U.S. would have had no right to shoot it down. The aircraft was flying within Iranian airspace and did not follow a path that could be considered an attack profile, nor did it illuminate the Vincennes with radar. During the incident, the Vincennes had also covertly entered Iranian territorial waters without first declaring war, while aiding Iraq's 1980–1988 war against Iran.Regardless of any mistakes made by the crew, the U.S. was fully responsible for the actions of its warship under international law.
Iran pointed out that in the past "the United States has steadfastly condemned the shooting down of aircraft, whether civil or military, by the armed forces of another State" and cited El Al Flight 402, Libyan Arab Airlines Flight 114 and Korean Air Lines Flight 007, among other incidents. Iran also noted that when Iraq attacked the USS Stark, United States found Iraq fully responsible on the grounds that the Iraqi pilot "knew or should have known" that he was attacking a U.S. warship.

 http://www.dailykos.com/story/2014/07/18/1314985/--I-Will-Never-Apologize-Iran-Flight-665-Shot-Down-290-Dead#