At least two people in Wellington have lost hundreds of thousands of dollars after being scammed into buying overseas shares.
The police said the scam was one of two serious fraud complaints being investigated.
Constable Ross Barnett said in one case the victim was called by an unknown person in Hong Kong and was offered to purchase shares, with the promise of large returns.
Mr Barnett said he was aware of at least one other person becoming involved with the same Hong Kong company, but they have yet to contact police.
He said the police were also investigating another scam, where a New Zealander met a person through an online dating site and unknowingly transferred stolen funds into offshore bank accounts.