The 85-year-old victim received a call from a man, claiming to be from his bank.
The man told the pensioner his account was at risk and he needed to transfer his savings.
The victim did not do so but was called by a second man who made the same request.
The 85-year-old later visited his building society in Wakefield and unwittingly transferred a large amount of money.
His relative became aware of what had happened and reported the fraud to the police.
Detective Inspector Tim Hunt of Wakefield CID: “This is clearly a very serious and sophisticated offence in which fraudsters have gone to some lengths to con the victim who was, quite rightly, initially suspicious.”
He warned people to be wary of similar scams.
Det Insp Hunt said: “We are investigating this offence with the banks in question and I would urge residents to be wary of this scam.
“Please remember that your bank and the police will never ask you to give your account details, pin and security code over the phone.
“If you receive a call from someone asking for this information and other details such as passwords then do not give it. Please end the call immediately and report the matter to the police, along with the number you were called on, if you have it.
For more information on how to protect yourself from bank and online fraud, visitwww.westyorkshire.police.uk/blockthewebmonsters