Kiwis are being targeted by scammers claiming to be from the New Zealand Police and Spark.
The caller claims to be targeting internet fraud and convinced victims to buy multiple iTunes cards and provide the numbers to them.
The scammer then redeems the cards and hangs up on the victim while maintaining access to their computer.
Acting Senior Sergeant Beth Purcell called for people to be wary of the latest telephone scam.
"This is a variation on previous scams seen by police, where the scammer claims to be from a widely recognised organisation in order to gain the victim's trust. These scams run constantly and while most people will not respond or buy into them, some people are more vulnerable," she said.