Center Township is one of fifteen townships in Greene County, Indiana, USA. As of the 2020 census, its population was 3,180, down from 3,535 at 2010.
According to the 2010 census, the township has a total area of , of which (or 100%) is land and (or 0.02%) is water. The streams of Anderson Branch, Bridge Creek, Indian Creek and Little Clifty Branch run through this township.
(This list is based on USGS data and may include former settlements.)
The township contains eight cemeteries: Beech, Bingham, Burch, Carmichael, Flynn, Lawrence, Sparks and Stone.