As of the census of 2000, there were 1,105 people, 405 households, and 249 families residing in the town. The population density was 219.3 people per square mile (84.7/km²). There were 519 housing units at an average density of 103.0/sq mi (39.8/km²). The racial makeup of the town was 79.19% White, 17.92% African American, 0.45% Asian, 0.09% Pacific Islander, 1.81% from other races, and 0.54% from two or more races. Hispanic or Latino of any race were 2.81% of the population.
There were 405 households out of which 22.2% had children under the age of 18 living with them, 51.9% were married couples living together, 7.7% had a female householder with no husband present, and 38.3% were non-families. 36.3% of all households were made up of individuals and 17.5% had someone living alone who was 65 years of age or older. The average household size was 2.28 and the average family size was 2.72.
In the town the population was spread out with 32.2% under the age of 18, 7.1% from 18 to 24, 21.4% from 25 to 44, 22.6% from 45 to 64, and 16.7% who were 65 years of age or older. The median age was 37 years. For every 100 females there were 89.9 males. For every 100 females age 18 and over, there were 92.5 males.
The median income for a household in the town was $37,411, and the median income for a family was $47,143. Males had a median income of $40,236 versus $24,821 for females. The per capita income for the town was $19,531. About 10.5% of families and 17.3% of the population were below the poverty line, including 12.8% of those under age 18 and 14.0% of those age 65 or over.
Grundy is served by the Grundy Municipal Airport located in Vansant. The airport serves general aviation air traffic. Commercial air traffic can be found at airports in Bluefield (1 hour driving away) and Beckley (2 hours driving away) in West Virginia and at the Tri-Cities Regional Airport in Tennessee (about 2 hours driving away).
Four County Transit maintains a local trolley system that services downtown locations. Stops include the Courthouse, Grundy Church of Christ, the former Food City parking lot, the Grundy Community Center, the Appalachian School of Law, and the former downtown parking lot.
Grundy is at the corner of the Levisa River and Slate Creek. The Norfolk Southern Railway maintains tracks and runs trains through the town but no trains stop in Grundy.
Grundy is served by U.S. Highway 460. The Coalfields Expressway will be built just to the north and east of town. State Route 83 is also a major highway in the area.