The scammers called under the guise of being from the phone company's customer service, or frmo the former police organisation OFCANZ (Organised and Financial Crime Agency).
Police say the scammers tell their victims their computer has been targeted by hackers and they need remote access to fix it.
Grant McBeath, Spark's customer channels manager, said that the scammers had nothing to do with the company.
"They like to use our name because so many New Zealanders have a Spark account."
Police said anyone, who suspected they were being scammed, should hang up immediately.
Often it was older and more vulnerable members of our communities who were targeted and became victims of scams, a police media release said.