Six incidents have been reported to police between 3 and 13 February.
In all the cases, two or three men have targeted foreign national tourists in an attempt to steal money - succeeding on two occasions.
The men, who are described as southern European, claimed to be police officers before demanding to search the victims.
Police Scotland said the first incident took place at about 13:20 on 3 February in the Grassmarket, when a Chilean man was approached by a man who asked him to take his photograph.
The pair were then approached by two suspects who claimed to be police officers and then demanded to search them.
The two police impersonators then got into a silver or grey Seat hatchback and drove away and the other man walked into the Grassmarket.
Officers said the Chilean man later realised a three-figure sum of money had been stolen from him.
On 13 February, two Chinese tourists lost a four-figure sum of cash when they were targeted in a similar scam on Market Street. They were approached by two men who showed them ID and said they were undercover police officers.
Other incidents happened in Chambers Street, Castle Street, and in the Calton Hill area. There was one incident on 3 February, one on 11 February and four on 13 February.
Sgt Mark Hamilton, of Police Scotland, said: "These men are purposely targeting tourists who are visiting the city centre in a bid to steal money from them.
"Impersonating a police officer is not only inappropriate, it is illegal. We would advise that if you are stopped by someone claiming to be a Police Scotland officer, request their collar number and ask to see a warrant card.
"All our officers are happy to provide this information to the public and it should be offered readily."
Police in Edinburgh are investigating a series of thefts and attempted thefts where men have impersonated police officers.