The sentence "over-emphasised" the crimes, and Hewitt's age and health should be considered, his lawyer said.
The prosecution said it was opposed to the sentence being reduced.
The 76-year-old, who is out on bail, was convicted last year of raping and sexually assaulting girls he coached in South Africa the 1980s and 1990s.
The trial judge gave him permission to challenge his sentence, but not conviction, in the Supreme Court of Appeal.
Last month, the Australian-born Hewitt was expelled from the International Tennis Hall of Fame because of his conviction.
"The crux of the matter is that age is supposed to be taken into account," his lawyer Johann Engelbrecht told a panel of three judges who are hearing the appeal.
"Our submission is that the sentence over-emphasises the crime and the retribution," he added.
'No remorse'
Mr Engelbrecht also argued that Hewitt had not committed one of the "worst offences", and was not a danger to society, South Africa's privately owned Times Live news site reports.
The judges questioned the lawyer's views, with one remarking that the trial judge could have sentenced Hewitt to life in prison for raping a minor, it reports.
Prosecutor Carina Coetzee said Hewitt did not deserve a lower sentence because he had failed to show remorse, and had breached the trust of children.
Hewitt was found guilty in March last year of raping two girls and of sexually assaulting a third.
The trial judge said at the time that the striking similarities between the three victims' testimonies showed that his conduct was calculated.
The appeal court reserved judgement. It has the power to maintain the six-year sentence, reduce it, or increase it.
Hewitt played initially for Australia, later moving to South Africa and taking citizenship there.
He was a member of the South African team which won the Davis Cup by default in 1974.
India, their opponents, refused to travel to South Africa for the final as a protest over the government's apartheid policies.
Former Wimbledon tennis champion Bob Hewitt has appealed in a South African court against his six-year prison sentence for raping under-age girls.