25 May 2015 Last updated at 11:53 BST
They were found near Nuneaton after a tree had fallen down.
They are about three weeks old and should be released within the next four weeks.
Catherine Clements and Geoff Grewcott from the Nuneaton and Warwickshire Wildlife Sanctuary told BBC Midland Today's Laura May McMullen that the chicks need feeding every hour.
An animal sanctuary in Warwickshire is hand rearing five Greater Spotted Woodpecker chicks so they can be released back into the wild.