Damon is a census-designated place (CDP) in Brazoria County, Texas, United States. The population was 552 at the 2010 census.
The Karankawa people lived on Damon Mound before the arrival of Europeans. Arrowheads, burial grounds, broken pottery, and stone tools found in the area are evidence of their habitation. In ancient times, the mound's sour earth was regarded by the local native peoples as having medicinal properties. This feature was caused by the presence of sulphur and other minerals near the surface.The area was first settled by Europeans in 1831 when Samuel Damon arrived from the United States. Damon married Lorena Darst and built a home on the south side of the mound. The settlement grew until it counted 100 inhabitants in 1890 when it was called Damon Mound. At that time cattle ranching was an important business. In 1895, the post office reopened after having been closed for three years. The town was renamed Damon around that time. A Baptist church opened in 1896. In 1918 a railroad line was built from Rosenberg to Damon in order to haul away the limestone and sulphur that were quarried from the mound. In 1925 the town had 300 residents and a Catholic church was founded.