Greenville is named after its founder, John Green, who settled in the wilderness of the southwest section of the lower peninsula of Michigan in 1844. John Green constructed a sawmill on the Flat River that is credited for attracting other settlers. The newly formed Green’s Village attracted many people of Danish origin who followed another early Danish settler’s positive letters home regarding the area.
Greenville celebrates the Danish Festive on the third weekend of August.
Greenville is the home of the first Meijer's grocery store as well as its founder Fred Meijer.
According to the United States Census Bureau, the city has a total area of 15.4 km² (5.9 mi²). 14.8 km² (5.7 mi²) of it is land and 0.6 km² (0.2 mi²) of it is water. The total area is 4.03% water.
As of the census of 2000, there are 7,935 people, 3,303 households, and 2,041 families residing in the city. The population density is 536.6/km² (1,389.2/mi²). There are 3,571 housing units at an average density of 241.5/km² (625.2/mi²). The racial makeup of the city is 96.16% White, 0.54% African American, 0.54% Native American, 0.32% Asian, 0.08% Pacific Islander, 1.16% from other races, and 1.21% from two or more races. 3.25% of the population are Hispanic or Latino of any race.
There are 3,303 households out of which 31.7% have children under the age of 18 living with them, 42.5% are married couples living together, 14.6% have a female householder with no husband present, and 38.2% are non-families. 32.2% of all households are made up of individuals and 13.9% have someone living alone who is 65 years of age or older. The average household size is 2.35 and the average family size is 2.95.
In the city the population is spread out with 25.4% under the age of 18, 10.2% from 18 to 24, 28.1% from 25 to 44, 19.3% from 45 to 64, and 17.0% who are 65 years of age or older. The median age is 35 years. For every 100 females there are 90.3 males. For every 100 females age 18 and over, there are 83.8 males.
The median income for a household in the city is $30,453, and the median income for a family is $35,050. Males have a median income of $32,500 versus $23,338 for females. The per capita income for the city is $15,933. 15.2% of the population and 9.4% of families are below the poverty line. Out of the total people living in poverty, 24.1% are under the age of 18 and 6.6% are 65 or older.