The teenager was at home with her father in Chorley just after 6pm last Monday when the fake cops knocked on the door bearing false ID cards.
After handcuffing her dad, the robbers led the young girl outside and forced her into a black Ford C-Max.
The suspects then robbed the family's home of £3,600 in cash, and three mobile phones.
The youngster was returned to the house unharmed after the robbery.
Sgt Andy Bramhall from Chorley police warned members of the public to thoroughly check ID cards which are shown to them, saying: "It is important people meticulously scrutinize any ID cards which are presented to them, and if they are concerned to contact us."
He also told the Chorley Guardian that he appealed for anyone with any information about the incident to come forward.
What a terrifying experience for this young girl!