Glamorgan chairman Barry O'Brien says the SSE Swalec Stadium has earned the right to hold Ashes Tests regularly.
The Cardiff venue will host the opening match of the 2015 series between England and Australia on 8 July.
Glamorgan's home first hosted an Ashes match in 2009 but missed out in 2013.
"We're not going to get an Ashes every time," O'Brien said. "But I think if we can get one every other time, it's what we deserve and that would keep everyone happy."
Lord's, Trent Bridge, Old Trafford, Chester-le-Street and The Oval were the Ashes venues in 2013.
This time, Cardiff and Edgbaston have been selected, with Old Trafford and Chester-le-Street missing out.
Headingley, having missed out in those two series, will return as a venue for the 2019 Ashes series alongside Old Trafford, Lord's, The Oval and Edgbaston.
That leaves Hampshire's Rose Bowl as the Test venue to have missed out in the previous three home Ashes series.
The England and Wales Cricket Board has invited tenders for the allocation of major matches between 2020 and 2023, which includes the next Ashes series in 2022.
But despite the fierce bidding competition, O'Brien told BBC Radio Wales Sport that he is hopeful a lucrative Ashes match will return to Cardiff then.
"We do press very hard the fact that we are an international stadium, we are the 'Wales' in the England and Wales Cricket Board and we put on a fantastic show last time round," he added.