The founder of Metro Bank, Vernon Hill, who posed with his dog to publicise the bank when it first opened, will be replaced as chairman, the bank says.
The bank had "reached a size and scale where it is appropriate to appoint an independent chair", Mr Hill said.
The bank also reported a sharp drop in first half profits, following a major accounting error earlier this year which shook confidence in the bank.
Customers withdrew £2bn of deposits over the six months to June.
Half year pre-tax profits fell to £3.4m from £20.8m a year earlier, the bank said.
Mr Hill, an American, set up Metro Bank to challenge the UK's traditional banks.
The lender, which presents a less stuffy image than traditional banks, grew rapidly in the first few years after its launch, but in January it revealed it had miscalculated the risk level of some of its commercial loans and required additional shock-absorbing capital to support them. In May it turned to investors to raise £375m of new capital.
Mr Hill, who will continue as chairman until his successor is appointed, became the face of the new bank when it was launched in 2010 shortly after the financial crisis.
Its branches were branded with bold red, white and blue colours and there were posters of Mr Hill's Yorkshire Terrier Sir Duffield - officially the bank's "chief canine officer" - advertising its policy of welcoming dog owners.
Metro Bank chose an unusual strategy, building a network of more than 60 physical branches, which open earlier and longer than its rivals', at a time when most banks were scaling back their High Street presence.
The bank said Mr Hill would remain as a non-executive director and president after he steps down as chairman.
While the chairman "leads the board and is responsible for its effectiveness and governance", Metro Bank said, as president, Mr Hill "will continue to instil, challenge and drive the Metro Bank model".
"Vernon is the inspiration behind Metro Bank, the first High Street bank to open in the UK in over 100 years," said Sir Michael Snyder, a senior independent director at Metro.
But he said the board shared Mr Hill's view that it was time to appoint an independent chairman to "oversee the next stage of our journey".
- Metro Bank opened its first branch in London's Holborn in 2010 in the wake of the financial crisis
- It was the first High Street bank to open in the UK in more than 100 years
- It is one of so-called challenger banks to the big High Street names, and opens seven days a week
- Founder Vernon Hill shook up the US banking scene in 1973 when, aged 26, he founded Commerce Bank with one branch
- When he sold Commerce Bank in 2007 for $8.5bn, it had 440 branches