Television New Zealand is marketing them in a prime-time slot as Britain's "fattest and laziest family".
But the stars of the show - a family of four who collectively weigh almost 500kg - have lashed out at the broadcaster, saying there are fatter families in Britain.
The Chawner family, from Blackburn, went public with their weight battle last year on a British series called Lorraine Kelly's Big Fat Challenge after being persecuted by the public for their lifestyle.
Last month, TVNZ started screening the show Big Fat Family Challenge with the description "the Chawners, labelled Britain's fattest and laziest family".
Philip Chawner, 56, told the Herald he was disgusted how TVNZ had marketed the show because "we are absolutely not Britain's fattest family".
"We was labelled ... We feel disgusted about it, because we was just trying to lose weight. It's our story and we just want to put it right," he said.
The Chawners have been ridiculed in Britain because no one in the family works and they all live on benefits.
Mr Chawner, who weighs about 135kg, found out that the show was being screened in New Zealand when he was contacted by a New Zealand fan over Facebook. The fan loved the show, but not how it was labelled.
"We've had a lot of feedback from people in New Zealand who all say they like the show, but it's not fair how we've been targeted as the 'fattest family' because it's not true and it's a total lie," he said.
"We're definitely not the fattest family in England because there was a woman on our local TV this week, she was 51 stone [323kg] but they're calling us the biggest family."
He said the family agreed to do the show after he developed diabetes and could no longer work. They wanted to get healthier and to lose weight.
Mr Chawner said the TVNZ label brought back memories of when his daughter Emma appeared on talent show The X Factor in 2009 and the family were called "the real Teletubbies" and "lard buckets" by the British press.
"We've come so far since then."
Mr Chawner's 23-year-old daughter, Samantha, said the family wanted an apology from TVNZ.
A TVNZ spokeswoman did not apologise but said the broadcaster marketed the programme based on the materials delivered by the international distributor.
'Big Fat' father slams TVNZ promotion
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