Commonwealth Bank chief executive Matt Comyn is sending letters to customers inviting them to contact him personally with their complaints.
In a letter to be sent out over the next few weeks, Mr Comyn acknowledges the bank has made mistakes - many of which have been publicly aired at the financial services royal commission.
"Over the last few months, the banking industry, including the Commonwealth Bank, has been rightly criticised for mistakes we've made," Mr Comyn wrote.
"You may have seen examples of this in the news."
Mr Comyn, who became chief executive this year after Ian Narev quit following allegations the bank broke money-laundering laws, apologised to customers for mistakes over the years.
"I'm sorry for the mistakes we've made," he wrote.
"My job now is to fix them."
Revelations from the royal commission have included Commonwealth Bank advisers charging dead clients fees in 2015, plus more than 13,000 criminal breaches of superannuation law.
Mr Comyn's pledge comes a week after rival NAB kept variable mortgage rates on hold in an effort to gain favour with customers.
This was despite Westpac, Commonwealth Bank and ANZ saying they would raise their standard variable rates in response to funding costs.
NAB chief executive Andrew Thorburn said the decision was made to restore trust.
