Neill Smith Brown (April 18, 1810 - January 30, 1886) was governor of Tennessee from 1847 to 1849.

Neill Brown was born in Giles County, Tennessee. He taught school in his native county to work his way through college. He was admitted to the bar in 1834, and later fought with the 1st Tennessee in the Seminole War. He was a member of the state legislature from 1841 to 1847, prior to his receiving the nomination of the Whig Party for governor of Tennessee. He defeated the incumbent Democratic governor, Aaron V. Brown. Development of telegraph service began around this time. A law was passed by the legislature during his administration calling for true public schools to be established throughout the state, but it was left to local governments to implement the provisions of this law, and very little was to come out of it.

Brown was defeated for re-election in 1849 by Democrat William Trousdale. He was later U.S. minister to Russia and again served in the state legislature. He also served as a delegate to the state constitutional convention of 1870 which composed the current constitution of Tennessee. His younger brother, John C. Brown, served as governor of Tennessee from 1871 to 1875.