Francis Napier, 6th Lord Napier (1702–1773) was a Scottish peer.
Born Francis Scott, he was the son of Sir William Scott, 2nd Baronet of Thirlestane, and Elizabeth Napier, Mistress of Napier. Upon the death of his maternal grandmother Margaret Brisbane, 5th Lady Napier, he achieved the title Lord Napier and changed his last name to Napier; upon the death of his father in 1725, he achieved the title Baronet Scott, of Thirlestane in the County of Selkirk. The titles have been united ever since.
Lord Napier married twice, firstly in 1729 to Lady Henrietta Hope, the daughter of Charles Hope, 1st Earl of Hopetoun and Henrietta Hope, Countess of Hopetoun. They had five sons:
- William Napier (d. 1775) who became the 7th Lord Napier in 1773
- Charles Napier of Merchiston Hall (1731 - 1807), a Captain in the Royal Navy
- Lt. Col. Francis Napier (d. 1779)
- John Napier (d. 1759)
- Major General Mark Napier (1738 - 1809)
In 1750, he married Henrietta Maria Johnston, the daughter of George Johnston of Dublin, and had:
- George Napier, who married Lady Sarah Lennox and whose sons were notable in their military service
- Hester Napier (d. 1819)
- James Napier (d. 1760)
- Patrick Napier (d. 1801), a Captain in the Royal Navy
- James John Napier (d. 1776)
- Stewart Napier (d. 1778)
- Mary Napier (d. 1765)
Upon his death in 1773, his titles passed to his eldest son William.