The Conservatives' Dawn Barnett, a councillor in Brighton and Hove, says those on "really good" benefits were abusing the service and cheating those who needed it more.
She said she had only witnessed one example where she felt someone had taken food they didn't need, when she drove someone from a neighbouring ward to a food bank.
Councillor Barnett told Premier: "I took her to the food bank, which was in Brighton. She collected seven huge bags of food, and when I dropped her back to her home she said thank you very much I really appreciate that, it saved me getting a taxi.
"When I looked at the box outside her house she'd got beer cans and wine bottles and I thought...if she could afford a taxi that wasn't a necessity for me to take her to a food bank.
"I think it really needs tightening up on the people that go there...There are people more deserving."
The Trussell Trust, a Christian organisation that runs the majority of the UK's foodbanks, denied Councillor Barnett's claims by saying they only serve people who are referred to them by medical professionals.
Hear from Councillor Barnett: