An inbred maize line, designated PH6HR, the seeds and plants of inbred maize line PH6HR, methods for producing a maize plant, either inbred or hybrid, produced by crossing the inbred maize line PH6HR with another maize plant, and seed and plants produced therefrom. The invention also relates to methods for producing a modified PH6HR maize plant that comprises in its genetic material one or more transgenes or backcross conversion genes and to the transgenic and backcross conversion maize plants produced by these methods. This invention also relates to methods for producing other inbred and hybrid maize lines derived from inbred maize line PH6HR and to the inbred and hybrid maize lines so produced.