Sir Robert Phelips (c. 1586–1638) was an English politician. He was the son of Sir Edward Phelips, Speaker of the House of Commons and Master of the Rolls. Knighted in 1603, he was the Member of Parliament for East Looe (1604–11), Saltash (1614), Bath (1621–22) and Somerset (1624–25 and 1628–29).
In his later Parliaments Phelips was one of the leading spirits in the House of Commons and an opponent of James I, Charles I and their adviser Buckingham. In 1622 he supported the Commons petition against the Spanish marriage, and was arrested soon after Parliament was dissolved, being imprisoned in the Tower of London for several months. When the next Parliament was summoned, the King demanded that Phelips (and a number of others) should not be returned but, although he had influence with the boroughs James could not intimidate the county freeholders and Phelips was elected for Somerset. In the 1625 Parliament, first of the new reign, he was the outstanding leader of the anti-Court party so that Gardiner in his History of England said that "As far as the history of such an assembly can be summed up in the name of any single man, the history of the Parliament of 1625 is summed up in the name of Phelips."
For the 1625–26 Parliament, the Crown adopted a wiser stratagem, ensuring that Phelips was named as High Sheriff of Somerset which debarred him from election. Nevertheless, he was once again named as Somerset's choice and attempted to take his seat; but in this case the law was clear and he was duly excluded. He returned, however, in the next Parliament, taking a prominent part again though ceding the informal leadership of the opposition to Sir John Eliot.
Robert's son, Edward Phelips, was the MP for Ilchester and Somerset.