The planes, which are believed to be MiG-21 and MiG-23 jets, are capable of flying although it is unclear if they are equipped with missiles, according to the Syrian Observatory for Human Rights.
The jets were seized from Syrian military airports now under IS control in the northern provinces of Aleppo and Raqa, according to the Britain-based group, which has a wide network of sources inside the war-torn country.
It said that former Iraqi army officers who once served under Saddam were supervising the training at the military airport of Jarrah, east of the city of Aleppo.
Witnesses have reported seeing planes flying at a low altitude to avoid detection by radar after taking off from Jarrah.
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It comes as the United States and its allies carry out a wave of air strikes on IS positions in Syria and Iraq.
The jihadists also control two other airports in Syria -- Albu Kamal near the Iraqi border and Tabqa in Raqa province.
IS has captured large parts of Syria and Iraq, committing atrocities and declaring an Islamic "caliphate".
After the US-led invasion of Iraq in 2003, some Sunni former officers from Saddam's army joined the ranks of the Islamic State of Iraq, a branch of Al-Qaeda which later became IS.