Francis Godolphin, 2nd Earl of Godolphin, PC (3 September 1678 – 17 January 1766) was a British nobleman and politician, styled Viscount Rialton between 1706 and 1712.
Godolphin was the only child of Sidney Godolphin, 1st Earl of Godolphin. He was born in Whitehall, London, on 3 September 1678, and baptised the same day. His mother, Margaret Godolphin, died six days later on 9 September. John Evelyn, who had been her most intimate acquaintance, transferred his friendship to her infant son, took charge of the general superintendence of his education, and continued to take an interest in his welfare as he grew.
Francis Godolphin was educated at Eton College, and at King's College, Cambridge, where he took his M.A. degree in 1705. His first public appointment was that of joint registrar of the court of chancery on 29 June 1698, which he held to 20 January 1727, holding also the place of one of the tellers of the exchequer from 1699 to 1704. He was chosen a member of parliament for East Looe in Cornwall on 1 December 1701, but on 4 February 1701–2 elected to serve for Helston, and sat for that constituency till 21 September 1710. As cofferer of the household he was in office from 1704 to 1711, and acted as lord warden of the stannaries, high steward of the duchy of Cornwall, and rider and master forester of Dartmoor from 1705 to 1708. He was known under the courtesy title of Viscount Rialton from 29 December 1706 till 1712. He sat for the county of Oxford from 1708 to 1710, and for Tregony in Cornwall from the latter date until he was elevated to the upper house as second Earl of Godolphin on the death of his father on 15 September 1712.