Glenwood Township was named for the glen and woods within its borders.

As of the census[1] of 2000, there were 1,004 people, 408 households, and 301 families residing in the township.

There were 639 housing units at an average density of 15.9 per square mile (6.1/km2).

There were 408 households, out of which 29.7% had children under the age of 18 living with them, 65.9% were married couples living together, 4.2% had a female householder with no husband present, and 26.2% were non-families.

23.8% of all households were made up of individuals, and 13.0% had someone living alone who was 65 years of age or older.