As of the census of 2000, there were 15,198 people, 6,641 households, and 4,097 families residing in the town. The population density was 417.9/km². There were 7,212 housing units at an average density of 513.6/sq mi (198.3/km²). The racial makeup of the town was 92.03% White, 5.74% African American, 0.19% Native American, 0.54% Asian, 0.02% Pacific Islander, 0.88% from other races, and 0.60% from two or more races. Hispanic or Latino of any race were 1.49% of the population.

Depot Street, part of the Greeneville Historic DistrictThere were 6,641 households out of which 25.5% had children under the age of 18 living with them, 44.6% were married couples living together, 13.9% had a female householder with no husband present, and 38.3% were non-families. 34.5% of all households were made up of individuals and 16.1% had someone living alone who was 65 years of age or older. The average household size was 2.18 and the average family size was 2.78.

In the town the population was spread out with 21.3% under the age of 18, 7.7% from 18 to 24, 26.3% from 25 to 44, 24.3% from 45 to 64, and 20.4% who were 65 years of age or older. The median age was 41 years. For every 100 females there were 84.4 males. For every 100 females age 18 and over, there were 79.5 males.

The median income for a household in the town was $25,999, and the median income for a family was $36,129. Males had a median income of $30,629 versus $21,425 for females. The per capita income for the town was $17,126. About 16.5% of families and 20.7% of the population were below the poverty line, including 28.5% of those under age 18 and 18.0% of those age 65 or over