The sharp rise followed a change in the law under the last Government which scrapped fees for those bringing appeals against family visitor visas.
As a result the taxpayer has funded all such appeals since 2002.
Around 50,000 people last year challenged a decision not to give them a family visitor visa, which provides a temporary stay in the UK with a relative who lives here.
That was up from around 8,000 in 2002.
The appeals cost the public a total of £50 million in 2009, according to the report by Migration Watch UK.
The campaign group called for a tightening of the rules surrounding family visitor visas and for charges to be reinstated.
Sir Andrew Green, chairman of Migration Watch, said: “At a time of severe financial stringency for UK families it is an outrageously generous system which taxpayers should no longer be expected to fund.
“It should be stopped immediately, the definition of “family visitor” tightened, charges reintroduced and consideration given to bonds to ensure people actually leave at the end of their visit.”
The report said the definition of who was classed as a family member under the visa regime was so wide that it could cover up to 120 relatives for one individual.
As well as an applicant’s immediate family, such as parents or children, it can also include uncles, aunts, cousins, relatives of the applicant’s spouse and step family.
Fees for appeals against refusal were originally set at £500 for an oral hearing or £150 for a paper application.
They were cut to £125 and £50 respectively in 2001 before being scrapped altogether in 2002.
In the last four years the success rate of appeals has ranged between 28 per cent and 45 per cent.
Sir Andrew added: “The government have at last seemed to realised that it is ludicrous and grossly unfair that taxpayers are expected to foot the bill for foreign citizens who wish to visit Britain.
“In these straightened times there are much better uses for our money.
“The whole issue of immigration and asylum was so ineptly handled by the previous administration that it will inevitably take time to reverse some of its most woeful decisions but this must surely be one of the easier ones to accomplish and should be a high priority for Ministers.”