Originally known as Nina, Alvord adopted its present name in 1882 in honor of the president of the Fort Worth and Denver Railway. There is no connection with the Arizona bandit Burt Alvord. A post office was established in 1882. By 1890, Alvord was a retail center for area farmers. In 1925, Alvord had 1,376 residents (42 more than in 2010), a high school, an elementary school, four churches, and a weekly newspaper. The Burlington Northern Railroad stopped there.
The population dropped during the Great Depression because of a decline in watermelon farms and cattle ranches. In 1940, the population totaled 821, with 35 businesses; in 1960, e 720 people and 19 businesses; in 1990, 865 residents and 16 businesses. In 2000, the population was 1,007, with 62 businesses.