The airline company was founded in 2004 with the objective to execute air transport of passengers and cargo.

2005: After the completion of all the procedures with the Hellenic Civil Aviation (HCAA), the airline obtained the two certificates (Air Operator Certificate and Operating License) and leased an aircraft Boeing MD-82 of 161 seats.

During the winter period 2005–2006 operated charter flights connecting North Iraq with European cities.

During the winter period 2006–2007 operated charter flights based at Nairobi of Kenya to other capitals of Africa.

Alexandair operated charter services from Chania, Corfu, Heraklion, Kos, Thessaloniki, Rhodes and Erbil in North Iraq and Nairobi in Kenya.