Nelson was originally called Dent, after settler Richard Dent, and under the latter name was founded in about 1875. The present name is for Knute Nelson, a prominent citizen and afterward United States Senator from Minnesota. A post office was established as Dent in 1880, and in 1881 the name was changed to Nelson.
As of the census of 2010, there were 187 people, 84 households, and 45 families living in the city. The population density was. There were 92 housing units at an average density of. The racial makeup of the city was 98.9% White and 1.1% Native American. Hispanic or Latino of any race were 0.5% of the population. There were 84 households of which 25.0% had children under the age of 18 living with them, 38.1% were married couplesliving together, 11.9% had a female householder with no husband present, 3.6% had a male householder with no wife present, and 46.4% were non-families. 32.1% of all households were made up of individuals and 9.6% had someone living alone who was 65 years of age or older. The average household size was 2.23 and the average family size was 2.84. The median age in the city was 38.8 years. 20.3% of residents were under the age of 18; 11.3% were between the ages of 18 and 24; 29.5% were from 25 to 44; 26.2% were from 45 to 64; and 12.8% were 65 years of age or older. The gender makeup of the city was 54.0% male and 46.0% female.
2000 census
As of the census of 2000, there were 172 people, 73 households, and 44 families living in the city. The population density was 235.8 people per square mile. There were 76 housing units at an average density of 104.2 per square mile. The racial makeup of the city was 98.26% White, 1.16% Native American, and 0.58% from two or more races. Hispanic or Latino of any race were 0.58% of the population. There were 73 households out of which 24.7% had children under the age of 18 living with them, 50.7% were married couples living together, 6.8% had a female householder with no husband present, and 38.4% were non-families. 28.8% of all households were made up of individuals and 5.5% had someone living alone who was 65 years of age or older. The average household size was 2.36 and the average family size was 2.96. In the city, the population was spread out with 23.8% under the age of 18, 11.6% from 18 to 24, 32.0% from 25 to 44, 22.7% from 45 to 64, and 9.9% who were 65 years of age or older. The median age was 35 years. For every 100 females, there were 120.5 males. For every 100 females age 18 and over, there were 114.8 males. The median income for a household in the city was $34,375, and the median income for a family was $35,694. Males had a median income of $26,964 versus $28,438 for females. The per capita income for the city was $13,419. About 22.0% of families and 23.1% of the population were below the poverty line, including 35.6% of those under the age of eighteen and 8.7% of those sixty five or over.
