Ali Jafari, an 82-year-old who lived on the 11th floor of the block, is the latest victim to have been named by police as the recovery operation continues.
His identification was the 34th carried out by coroner Dr Fiona Wilcox.
Of those who died, the families of 18 victims have asked that their names not be released.
His family, including his wife, children and grandchildren have said he will be missed by them as well as the wider community.
A statement released on behalf of Mr Jafari's family reads: “Mr Ali Jafari, aged 82, died following being caught up in the fire at Grenfell Tower.
"Mr Jafari is survived by his wife, children and grandchildren. Ali was loved and will be greatly missed by his family and the wider community.”
The identification came a month after the fire took hold of the building on June 14.
Despite the efforts of around 250 firefighters, the 24-storey tower block, police believe around 80 people died in the fire.
Metropolitan Police Commander Stuart Cundy revealed around 255 people managed to escape the fire.
Mayor of London Sadiq Khan slammed Kensington and Chelsea Council on Thursday (July 13) for its handling of the survivors both immediately after the fire started and a month later.
He branded the council "inept and inadequate and close to being useless" during Mayor's Question Time at City Hall.
Keep up to date with the latest news in west London via the free getwestlondon app.
You can set up your app to see all the latest news and events from your area, plus receive push notifications for breaking news.