Coming top in the third session broadcast on Saturday, 10 May, they are now in contention for the competition's final grand prize of £10,000.
Ceri Rees is Capital City Jazz Orchestra's founder and saxophone player.
"This is the first time for us to take part in a competition such as Band Cymru, and it was fantastic to see a jazz band like us go up against wind and brass bands," says Ceri, who established the band seven years ago.
"There wasn't much activity in the jazz scene, in Cardiff or in Wales in general. Of course, there are small bands all over Wales, but what I wanted to do was bring together the Capital's best musicians to form a new band.
"We meet every first Tuesday on the month, upstairs in Dempsey's tavern, and there is a sell-out audience each month."
Despite the £10,000 end of series prize, money wasn't the incentive for entering the Band Cymru competition, says Ceri.
"It's true we're not competing for the money," he says. "What we wanted was to highlight that bands like ours exist in Wales. We believe that our musicians are among the best, and each one loves playing for the band."