John Alexander Greer (July 18, 1802 – July 4, 1855) was a Texan politician, and the second Lieutenant Governor of Texas serving under Governors George T. Wood and Peter H. Bell.Greer was born at Shelbyville, Tennessee on July 18, 1802. He was in Kentucky before moving to Texas in 1830. He represented San Augustine as a senator in the Congress of the Republic of Texas from 1837–1845.