According to the United States Census Bureau, the town has a total area of 3.8 square miles (9.9 km²), all of it land.
There were 1,181 households out of which 29.8% had children under the age of 18 living with them, 48.7% were married couples living together, 14.9% had a female householder with no husband present, and 32.9% were non-families. 30.1% of all households were made up of individuals and 12.4% had someone living alone who was 65 years of age or older. The average household size was 2.35 and the average family size was 2.87.
In the town the population was spread out with 22.6% under the age of 18, 8.7% from 18 to 24, 29.2% from 25 to 44, 20.7% from 45 to 64, and 18.8% who were 65 years of age or older. The median age was 37 years. For every 100 females there were 79.2 males. For every 100 females age 18 and over, there were 74.3 males.
The median income for a household in the town was $27,205, and the median income for a family was $34,234. Males had a median income of $32,443 versus $22,872 for females. The per capita income for the town was $15,478. About 12.5% of families and 15.5% of the population were below the poverty line, including 19.7% of those under age 18 and 14.0% of those age 65 or over.
Algood began as a small community known as White Plains in the early 1800s, which was built upon ancient Native American hunting grounds. The community benefited from its location along a branch of the Old Kentucky Road, which passed north-to-south across Middle Tennessee. By the late 1800s, the White Plains area was being called "Algood," named after a circuit rider who settled in the area around 1858. In 1899, the Algood Methodist Church (now Algood United Methodist Church) was built on land donated by the children of this early settler.