The 39 year-old has won praise for her singing skills after starring in the movie Country Strong and she performed at the recent relaunch of The Arts Club in London.
The Duke of Edinburgh, 90, is patron of the members-only club and was the guest of honour at a reopening party after its major refurbishment.
He was due to leave the party earlier but stayed on to hear the actress perform.
A source said to UK newspaper Daily Telegraph: 'One of the songs Paltrow sang was Forget You by Cee Lo Green, but she sang the original version, which is called F*** You.
'Before she sang it she said to the Duke: 'I hope you don't mind the lyrics - don't tell the Queen!''