Vietnam-born Anh Nhu Nguyen, 52, claimed he lost his wife and son in the inferno and was assigned a family liaison officer before police noticed inconsistencies in his story, Westminster Magistrates heard.
He tried to secure cash and both short and long-term accommodation from the funds reserved for the victims of the fire by Royal Borough of Kensington and Chelsea, prosecutors say.
Nguyen allegedly claimed he and become separated from his wife and 12-year-son on the smoke-filled stairwell and been prevented by firefighters from going back for them.
He said he had lived on the 15th floor of the tower for 20 years after emigrating to the UK from Hong Kong and that he had been making a cup of tea when the fire started.
Nguyen, who is a British citizen, is also accused of asking for clothes, shoes, food and electronic equipment from charities trying to help people left destitute by the blaze.
A man has appeared in court accused of trying to get a home and money by falsely claiming his wife and child had died in the Grenfell Tower disaster
The court heard how Nguyen attended on several meetings, claiming to live at flat 17 in the block.
Nguyen, of Beckenham, faces two counts of fraud by false representation. No pleas have been entered.
He is due at Southwark Crown Court for a pleas and case management hearing on 28 July.