Center Township is one of ten townships in Gibson County, Indiana. As of the 2020 census, its population was 1,317 (slightly down from 1,341 at 2010) and it contained 566 housing units. Francisco is the township seat.
According to the 2010 census, the township has a total area of , of which (or 99.63%) is land and (or 0.37%) is water.
The township trustee manages three cemeteries: Lawrence, Page, and Meade.
Center Township is served by the East Gibson School Corporation.