SunTrust said in a prepared statement it planned to drop the monthly fee on its "Everyday Checking" accounts beginning on November 2.
Any customers who incurred a fee since the charge was introduced in June would receive a full refund within the next 30 days, the bank said.
A SunTrust spokesman said the move was motivated by customer feedback.
Bank of America Corp, the second-largest U.S. bank by assets, said last week it still planned to impose a $5 monthly fee on customers, but would ease the requirements for having the fee waived.
Beginning October 1, banks were limited in what they could charge merchants for processing debit card transactions by the Durbin amendment, a key provision of the 2010 Dodd-Frank financial reform law passed by Congress.
Known as interchange fees, analysts project the change could cost the industry billions of dollars in annual fee income.
(Reporting by Joe Rauch in Charlotte, N.C.)