The Ministry of Consumer Affairs says scammers are moving from the internet to phonelines to try to trick people out of money.
Ministry spokesperson Richard Parlett says people tend to take phone calls more seriously than emails and are less likely to ignore the scam.
He says the ministry has had reports of several variations on a scam which promises a bank refund for an upfront fee.
Another phone scam which offers to remove computer viruses has reached one in every six New Zealanders.
Mr Parlett says people should hang up and notify the police if they get a suspicious call.