The airline said it began operations with a domestic flight from the southwestern city of Salalah to the capital Muscat.
In addition to the domestic market, SalamAir will fly to Dubai, as well as Mecca and Medina in Saudi Arabia, and Karachi in Pakistan, chairman Khalid al-Yahmadi told reporters.
The carrier is to operate a fleet of three leased Airbus A320 single-aisle planes.
Yahmadi said SalamAir could clinch between 20 and 30 percent of the Omani aviation market, currently dominated by the national carrier, Oman Air.