Sir Robert Salusbury, 1st Baronet (10 September 1756 – 17 November 1817) was a British Member of Parliament.
He was the eldest son of Robert Salusbury of Cotton Hall, Denbighshire and educated at Trinity College, Cambridge (1775) before studying law from 1776 at Lincoln's Inn, where he was called to the bar in 1785.
He was a Member of Parliament (MP) for Monmouthshire from 1792 to 1796 and for Brecon from 1796 to 1812. He was made a baronet on 4 May 1795 and was High Sheriff of Monmouthshire for 1786–87.
In 1780, he married Catherine, daughter and eventual heiress of Charles Van of Llanwern. They had three sons and two daughters. In 1816, he was jailed in the King's Bench Prison for bankruptcy and died at Canterbury in 1817.