Before joining the United States under the Texas Annexation in 1845, Texas was an independent nation known as the Republic of Texas. Seven cities served as its capital:

Washington (now Washington-on-the-Brazos), 1836

Harrisburg (now part of Houston), 1836

Galveston, 1836

Velasco, 1836

West Columbia, 1836

Houston, 1837–1839

Austin, 1839–1845 (also present-day capital of the State of Texas)

More Info: en.wikipedia.org