Waitematā's acting Detective Senior Sergeant Ben Bergin said scammers would pose as officers and try to extract personal details from the victim.
"The story changes slightly, but it will usually involve some sort of investigation and this 'officer' will report having located a valuable item of yours, such as a passport," he said in a statement.
"He will need your help or ask for your personal information. The caller speaks with an English accent and provides a bogus ID number to the victim."
Police arrested a number of people last year for a similar scam, which involved the scammers asking victims to withdraw cash as part of an "investigation."
"We strongly advise that you hang up," he said.
"From time-to-time, Police officers may contact you as part of their genuine duties. It can be a bit surprising to receive a call unexpectantly, so stop and think if you get a far-fetched story shared down the telephone line."
