As of the census of 2000, there were 1,276 people, 511 households, and 331 families residing in the city. The population density was 1,010.9 people per square mile (391.0/km²). There were 566 housing units at an average density of 448.4/sq mi (173.4/km²). The racial makeup of the city was 97.18% White, 0.31% Black or African American, 0.94% Native American, 0.31% Asian, and 1.25% from two or more races. Hispanic or Latino of any race were 0.24% of the population.
There were 511 households out of which 37.8% had children under the age of 18 living with them, 44.8% married couples lived together, 15.1% had a female householder with no husband present, and 35.2% were non-families. 29.7% of all households were of individuals and 16.8% had someone living alone 65 years of age or older. The average household size was 2.49 and the average family size was 3.06.
In the city the population was dispersed with 29.7% under the age of 18, 10.0% from 18 to 24, 30.2% from 25 to 44, 16.8% from 45 to 64, and 13.4% who were 65 years of age or older. The median age was 32 years. For every 100 females there were 95.7 males. For every 100 females age 18 and over, there were 87.3 males.
The median income for a household in the city was $34,830, and the median income for a family was $43,229. Males had a median income of $32,455 versus $22,750 for females. The per capita income for the city was $16,693. About 13.1% of families and 14% of the population were below the poverty line, including 18.1% of those under age 18 and 12.0% of those age 65 or over.
Generally, Braham residents gravitate to nearby Pine City or Cambridge for their shopping and services.