Gosport police warned the pair, in their 70s, lost the cash through a cryptocurrency scam.
Officers did not reveal the tactics the criminals used, but such frauds often invite people to buy into online currency such as Bitcoin to make a return.
But instead the cash goes straight to the criminals, and the money is lost.
On Facebook, Gosport police said: ‘Last week, one of our officers visited a couple, aged in their 70s, who had fallen victim to a cryptocurrency scam.
‘In total, the couple lost almost £20,000, leaving them without money they’d worked hard for – money they should be enjoying in their retirement.
‘Sadly, the couple in question were not the first to suffer from this type of fraud, and they likely won’t be the last.
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‘If you are thinking of investing in this area, please take a look at the below before making any decisions or parting with any cash.’
It comes as Money Saving Expert’s Martin Lewis warned this week on ITV show This Morning about the dangers.
He said: ‘It is very dangerous. It is psychological. These people are brilliant, if only these… horrible people could use their skills for something productive.’