The suspect, 26 and of no fixed address, was detained by West Midlands Counter Terrorism Unit officers after arriving on a flight from Turkey.
He is being held in custody in the West Midlands.
West Midlands Police said the arrest was pre-planned and there was no threat to the safety of the flight or the airport.
A man has been arrested at Heathrow Airport on suspicion of Syria-related terror offences, police have said.