Adelaide Lord Mayor Stephen Yarwood says he is tech-savvy but he got a rude shock when a $20,000 internet bill turned up after an overseas trip.

He forgot to turn off his international data roaming.

Mr Yarwood was in Taiwan for the Asia Pacific City Summit.

The bill most likely will have to be paid by ratepayers unless he can convince Telstra to waive it.

The mayor earns $128,000 annually but says he cannot afford to pay the bill himself.

"I can't afford to ... I have a mortgage, I have a family and I cannot afford a $20,000 bill," he said.

"To actually imply that I need to pay this back or to suggest that I'm anything other than the most frugal mayor in the entire country would actually be really unfair. I'm actually embarrassed and very sorry about it, but I physically can't afford to pay it back myself.

"I must stress that I'm very frustrated, embarrassed, because I'm tech-savvy and I've travelled with my mobile phone before."

City Councillor Anne Moran thinks Mr Yarwood should volunteer to pay half the bill.

"With all the sympathy in the world I would happily vote to pay for some of Stephen's bill, but I think he should pay for some of it too, it was his mistake," she said.