The FSA is inviting comments on the proposals
Banks could face league tables of poor service, under proposals published by the Financial Services Authority.
The watchdog said it was considering telling customers about the banks with the highest number of complaints and how well they dealt with them.
The plans have already received a positive response by the National Consumer Council (NCC).
But the British Bankers' Association said the plan could wrongly name and shame certain banks.
The proposals were outlined in a report into the FSA's work and the amount of information it discloses.
It currently operates under strict parameters in terms of the amount of detail made public, especially during investigations into the financial services industry.
But the FSA chief executive, Hector Sants, said: "We believe that transparency is an important regulatory tool, and as an organisation are committed to being open and transparent."
The move was praised by Steve Brooker, senior policy advocate of the NCC consumer group.
"The proposal to publish financial services firms' complaint records is welcome news and will encourage the industry to improve the way it deals with customers," he said.
"Companies will be encouraged to compete on quality and not just price."
But Peter Tyler, a policy director at the British Bankers' Association, said it would be extremely difficult to put the information in the correct context and make it useful for consumers considering whether to switch banks.
This would also go against the FSA's own intention not to name and shame banks, he said.
The FSA's proposals are in a discussion paper and the watchdog is calling for comments by 29 August.