The left-wing MP received ovations from the crowd for his messages on protecting benefits, ending austerity, raising taxes on the wealthiest and abolishing university tuition fees.
The rally on Tuesday ended the second day of his campaign visit to Wales.
Mr Corbyn is competing for the leadership against Andy Burnham, Yvette Cooper and Liz Kendall.
Earlier he addressed supporters in a gathering at the memorial stones to Welsh Labour hero and NHS creator Aneurin Bevan in Tredegar.
He praised the work of the Welsh Labour government in Cardiff Bay.
"I've been looking at their economic planning ideas, looking at the way they're trying to promote industrial development in Wales," he said.
"They need more powers in that area. They also need more resources, particularly in infrastructure improvements.
"If you want to have a growing economy, a better industrial economy, you have to improve the basic infrastructure, which is in main rail but in part road as well.
Mr Corbyn said he was keen to forge closer links between the Labour parties in Wales and Westminster, saying he knew the former First Minister Rhodri Morgan well.
He said he had admired Mr Morgan's attempts in office to create "clear red water" between the former UK Labour government's policies and a more traditionally socialist direction in Wales.
"Maybe we can narrow the red water and we can walk across it," he said.
Mr Corbyn said he was "absolutely" ready to meet First Minister Carwyn Jones, as the other three leadership contenders had done, when they were both available.
Ballot papers will be sent to Labour members and registered supporters on Friday with the result announced on 12 September.
About 1,000 people have attended a rally in Cardiff for Labour leadership candidate Jeremy Corbyn.