The meeting was orchestrated by the Treasurer's older brother, the Rev Tim Costello, who is currently head of World Vision Australia. He believes it could only be called "positive" if it translates into Australia increasing its aid commitment.
"The global movement against poverty is trade and aid because people from poor countries with HIV, malaria, [are] not able to get to school, access to clean water, can not trade or get access to markets without increases in aid," said Tim Costello.
Bono is renowned as an avid poverty campaigner, meeting with politicians from developed countries around the world and urging them to boost aid to poverty-stricken nations to 0.7% of GDP.
But the Irish rock star was not able to win over Mr Costello.
Peter Costello told Bono that Australia is doing its fair share by giving aid to Pacific neighbours; propping them up to ensure they're not failed states.
"We are practically the only country that gives aid in the Pacific. If we didn't focus our aid on the Pacific, the Pacific wouldn't be receiving aid at all," he told Bono.
After what was described as a "warm" hour-long discussion, the two departed.
Bono and rock band Pearl Jam recently performed a surprise duet at an open air concert on the sidelines of the Melbourne G20 summit, calling for an end to world poverty.
Church and aid groups joined in the protests as ministers and bankers began arriving.
Singing "Rockin' In The Free World", Bono called on 14,000 fans at the free "Make Poverty History Concert" to demand world politicians step up the fight against global poverty.
