SYDNEY, Nov 18 (Reuters) - Virgin Australia will position itself as a mid-market airline targeting around a one-third share of the domestic aviation market under the ownership of U.S. private equity firm Bain Capital, the airline's new chief executive said on Wednesday.

Virgin's shift from being a full-service carrier will mark the end of a decade-long arms race with rival Qantas Airways Ltd for corporate travellers involving lavish airport lounges, celebrity chefs and lie-flat business seats on longer domestic flights.

"Australia already has a low-cost-carrier and a traditional full-service airline, and we won't be either," new Virgin Australia Chief Executive Jayne Hrdlicka said in a statement, in reference to Qantas and its low-cost offshoot Jetstar.

"Virgin Australia will be a mid-market carrier appealing to customers who are after a great value airfare and better service," she said.

The country's second-biggest airline said it would introduce new on-board food purchase options in economy class but would retain business class seats and airport lounges in major cities and it will continue to include checked baggage in its economy-class fares. (Reporting by Jamie Freed; Editing by Sam Holmes)