Graham Township is one of ten townships in Jefferson County, Indiana, United States. As of the 2020 census, its population was 1,618 (slightly down from 1,668 at 2010) and it contained 705 housing units.
According to the 2010 census, the township has a total area of , of which (or 99.48%) is land and (or 0.52%) is water. The streams of Dry Branch, Lewis Creek, Little Creek, Neils Creek and Walton Creek run through this township.
The township contains three cemeteries: Carmel, Robertson and Valley.
It is in the Madison Consolidated Schools school district.
The zoned MCS elementary school is Deputy Elementary School. The zoned secondary schools of the Madison district are Madison Junior High School and Madison Consolidated High School.