Cleveland Run Township is a township in Cheyenne County, Kansas, United States.

Cleveland Run Township covers an area of 71.96 square miles (186.4 km2) and contains no incorporated settlements.

According to the USGS, it contains two cemeteries: Hackberry and Zion.

The stream of Valley Creek runs through this township.

This article about a location in Cheyenne County, Kansas is a stub.