Glenham is a town in Walworth County, South Dakota, United States.

[7] According to the United States Census Bureau, the town has a total area of 0.33 square miles (0.85 km2), all land.

There were 67 housing units at an average density of 203.0 per square mile (78.4/km2).

43.6% of all households were made up of individuals, and 18.2% had someone living alone who was 65 years of age or older.

32.1% of all households were made up of individuals, and 12.5% had someone living alone who was 65 years of age or older.

There were 9.3% of families and 13.9% of the population living below the poverty line, including 18.2% of under eighteens and none of those over 64.