Governor Conway may refer to:
Elias Nelson Conway (1812–1892), 5th Governor of Arkansas Henry Seymour Conway (1721–1795), Governor of Jersey from 1772 to 1795 James Sevier Conway (1798–1855), 1st Governor of Arkansas Thomas Conway (1735–1800), Governor of French colonies in India from 1787 to 1789 William B. Conway (1802–1839), Acting Governor of Iowa Territory