In a speech at the Nuffield Trust on Friday, Mr Hunt said that one of the last government's greatest mistakes was to set up the CQC to rate NHS organisations simply as 'compliant' or non-compliant'.
'The weeds of failure grow more quickly in a garden of mediocrity,' he told the Nuffield Trust conference. 'I believe our system fails to challenge low aspirations enough.'
A new Ofsted-style rating system for the NHS and the chief inspector of hospitals proposed in response to the Francis inquiry into failings in Mid Staffordshire would aim not just to root out poor practice, but also to champion excellence, he said.
For this reason, before the inquiry finished, Mr Hunt asked the Nuffield Trust to investigate 'whether and how it might be possible to rate and rank the excellence of care throughout the system'.
In response to a question from former Labour health minister Lord Norman Warner, Mr Hunt added that the last government was 'right to try to set up the star ratings system' to create a 'definition of success'.
Mr Hunt pointed back to the opening ceremony at the London 2012 Olympics, in which the NHS was hailed as 'one of the things that define us as a country'.
But he said the NHS must learn from Mid Staffordshire in the same way that Team GB Olympians responded to winning just a single gold medal at the 1996 Olympics with a huge cultural change.
'In 1996 we hit rock bottom and won just one gold medal,' Mr Hunt said. 'That was the moment everything changed. It wasn’t enough to turn up. We had to be the best - now we pretty much are.'
He added: 'Imagine if athletes focused not on winning, but not coming last. Too often the NHS does just that. By focusing on not coming last - avoiding the worst outcomes - we make those outcomes more, not less, likely.'
Mr Hunt said the chief inspector of hospitals proposed by the DH in response to the Francis report on the public inquiry into Mid Staffordshire NHS Foundation Trust would not only be responsible for rooting out failure, but also for promoting excellence.