According to The Times, the comedian puts £3.3 million each year into the Jersey-based K2 shelter, which is used by 1,100 tax avoiders.
Carr's lawyers confirmed his membership of the scheme but also added that it had been disclosed to relevant bodies and denied any wrongdoing.
The stand-up, who mocked Barclays' alleged tax avoidance in a 10 O'Clock Live sketch last year, allegedly pays himself an annual salary of £100,000 before sheltering the remaining £3.3m in the scheme.
It is claimed that four of the five companies controlled by Carr were set up by Blue Cube, itself part of the Peak Performance network of accounts which sells the K2 plan.
"It's a game of cat and mouse," said Roy Lyness of Peak Performance about the K2 plan.
"The Revenue closes one scheme, we find another way round it.
"It's like a satnav. I'm driving to Manchester, get a message saying there's a smash at Stoke, press this button to re-route."
He added: "That's all we do with tax avoidance. The revenue puts a block in, we just go round the block."
Watch Jimmy Carr's 2011 about tax avoidance on 10 O'Clock Live below: