The group, which owns Classic FM, is to bid for the new FM licence that regulator Ofcom is currently advertising with 107FM The Rock targeting over 35s with classic and contemporary rock music, ranging from Led Zeppelin to the Red Hot Chili Peppers.
But the new station would also support young musicians, encouraging bands to flourish and providing recording facilities to get their group's off the ground.
GWR has pulled together a board of local figures to spearhead the bid, including Peter Ellen, the managing director of record store chain Fopp, and Geoff Ellis, chief executive of T in the Park promoter DF Concerts.
Peter Taylor, president of the Edinburgh Chamber of Commerce and owner of the Town House Company, is also on the board alongside Karen Koren, managing director of the Gilded Balloon comedy venue.
They will senior GWR executives Roger Lewis, managing director and programme controller of Classic FM, Dirk Anthony, managing director of GWR content division Creation and Duncan George, managing director of the group's sales arm, Opus.
Ralph Bernard, executive chairman of GWR, said he wanted to fill a gap in the market in Edinburgh using the expertise that Classic FM used when it first entered the market over 10 years ago.
'Any new station faces significant challenges, but we're confident that we have listened to what our future listeners want and can bring a fantastic new station to Edinburgh,' he said.
But GWR will face competition from the majority of rival radio groups. Emap, the company that publishes Broadcast and owns radio stations Kiss and Magic, will bid with local consortium Castle FM.
SMG will put forward a Virgin Radio Classic Rock format and Celador Radio Broadcasting is bidding with the support of Who Wants to be a Millionaire host Chris Tarrant and former BBC Radio 2 controller Jim Moir.
The Guardian Media Group, Saga Radio and Scottish Radio Holdings are also expected to pitch for the new licence while Capital Radio has decided not to put forward a bid.
The closing date for applications is 23 September.