And last year, King Juan Carlos of Spain was removed as honorary president of the World Wildlife Fund after it emerged he had been hunting elephants in Botswana.
The International Fund for Animal Welfare, which campaigns for an end to trophy-hunting, said it was wrong for hunters like Gunton to glorify animals' suffering.
Spokeswoman Rebekka Thompson -Jones said: "The decision to kill an animal as social and intelligent as an elephant, just for fun is terrible enough.
"The obvious glorification makes it even more disturbing."
Gunton is chairman of the New Zealand Retail Property Group, and has developed shopping malls at Highbury on the North Shore and Tauriko in Tauranga, and the $1 billion Westgate town development at Massey.
He is also behind a controversial 16-storey property development in Milford. The Auckland Council has turned down a consent application for it, and it is going through the Environment Court.
Gunton was at his son's wedding in the South Island, and did not respond to repeated calls to his business, mobile phone and email address.
His business partner, Campbell Barbour, said it was a private matter.
"What some people will tell you is the fact that animals are effectively being protected for those purposes means the survival of a number of species is assured," he said.
It is unclear when and where the pictures were taken, but they were posted on to a website in 2011 and 2012 under the account of South African big game hunter Graeme Bruce Pollock.
