Atkinson Francis Gibson (20 November 1763 – 22 January 1829) was a British banker.
He was born in Saffron Walden, Essex, on 20 November 1763, the son of George Gibson and Elizabeth Robinson.
He ran the Saffron Walden and North Essex Bank.
On 1 October 1789 in Dunmow, Essex, he married Elizabeth Wyatt, the daughter of Jabez Wyatt of Saffron Walden.
They had five children:
- Wyatt George Gibson (1790–1862), banker
- Mary Gibson (1791-1839)
- Jabez Gibson (1794-1838), banker
- Ann Gibson (1799-1802)
- Francis Gibson (1805-1858), businessman
He died on 22 January 1829 and was buried at the Friends' Burial Ground, Saffron Walden on 22 January 1829.
From 1828, Gibson and his wife Elizabeth were responsible for laying out Bridge End Gardens on fields on the edge of Saffron Walden and covering an area of 2.7 hectares (7 acres).