According to the United States Census Bureau, the town has a total area of 0.8 square miles (1.9 km²), all of it land.
There were 240 households out of which 31.3% had children under the age of 18 living with them, 63.3% were married couples living together, 7.5% had a female householder with no husband present, and 25.8% were non-families. 25.8% of all households were made up of individuals and 16.3% had someone living alone who was 65 years of age or older. The average household size was 2.45 and the average family size was 2.92.
In the town the population was spread out with 26.6% under the age of 18, 6.8% from 18 to 24, 23.9% from 25 to 44, 22.0% from 45 to 64, and 20.8% who were 65 years of age or older. The median age was 40 years. For every 100 females there were 95.0 males. For every 100 females age 18 and over, there were 93.3 males.
The median income for a household in the town was $31,705, and the median income for a family was $39,063. Males had a median income of $30,577 versus $24,500 for females. The per capita income for the town was $15,593. About 9.4% of families and 13.2% of the population were below the poverty line, including 22.0% of those under age 18 and 11.8% of those age 65 or over.
There is a 19 story cross located next to Interstate 40 (formerly U.S. Route 66) at Groom. This tall free standing Cross can be seen from twenty miles (32 km) away. Surrounding the base of the Cross are life sized statues of the Stations of the Cross. Inspired by this cross, residents of Effingham, Illinois erected a similar cross that is eight feet taller. Many claim this cross to be the largest in the Western Hemisphere. However, it is smaller than the cross erected in the Valle de los Caidos in Spain, located at and elevated 152.4 m overground. The cross is also shorter than the cross at the Mission Nombre De Dios in St. Augustine, FL. The movie Leap of Faith was filmed on location near the cross in Groom.
Also in Groom one can find a leaning water tower which currently serves as a decorative item. It originally was a functioning water tower which was slated for demolition until Ralph Britten bought it and moved it to serve as a sign for his truck stop and tourist information center (located on a stretch of interstate that was once a part of U.S. Route 66). This truck stop can still be seen, set back off the road behind the tower, now boarded up and in disrepair. The leaning water tower still remains a popular target for cameras, and the town of Groom turns on a large colored star mounted on the top around Christmas time. The water tower is a common image from Route 66 photography books.