Sir Robert Barnham, 1st Baronet was an English politician who sat in the House of Commons from 1660 to 1679.
Barnham was the son of Sir Francis Barnham and his wife Elizabeth Leonard, daughter of Sampson Leonard of Chevening.
His father had been Member of Parliament for Maidstone. He was re-elected in 1661 for the Cavalier Parliament and sat until 1679. He was created a baronet, of Boughton Monchelsey in the County of Kent, on 14 August 1663.
Barnham married Elizabeth Henley, daughter of Robert Henley.
Barnham died in circa June 1685, aged 78. There is some uncertainty as to whether a supposed grandson, Robert Barnham, succeeded in the baronetcy or if it became extinct on Barnham"s death.
In 1660, Barnham was elected Member of Parliament for Maidstone in the Convention Parliament.