Montgomery is a town in Barr Township, Daviess County, Indiana, United States. The population was 343 at the 2010 census. As of the census of 2000, there were 368 people, 140 households, and 100 families residing in the town. The population density was 1,527.7 people per square mile (592.0/km). There were 153 housing units at an average density of 635.1 per square mile (246.1/km). The racial makeup of the town was 99.18% White, 0.27% African American, 0.27% Native American, and 0.27% from two or more races. Hispanic or Latino of any race were 0.82% of the population.