According to Warren Upham, Parke Township was probably named for an early settler.

As of the census[1] of 2000, there were 450 people, 167 households, and 134 families residing in the township.

The population density was 13.2 people per square mile (5.1/km2).

There were 167 households, out of which 35.9% had children under the age of 18 living with them, 75.4% were married couples living together, 1.8% had a female householder with no husband present, and 19.2% were non-families.

16.8% of all households were made up of individuals, and 5.4% had someone living alone who was 65 years of age or older.