Non‐aqueous redox flow batteries (RFBs) are emerging electrochemical technologies for grid energy storage. Non‐aqueous Mg RFBs that use Mg metal as the anode are especially promising due to various benefits of the Mg metal anode, including its low potential, high volumetric capacity, SEI‐free, highly reversible operation and low cost. Despite the potential, there are rarely any studies on developing non‐aqueous Mg RFBs. Herein, a non‐aqueous Mg redox flow battery using a polymer catholyte is reported. Through rational molecular engineering, a carbonyl‐based moiety is combined with a polyethylene glycol moiety to achieve a polymer with high voltage and high solubility in the ether‐based electrolyte. A series of polymers with different polyethylene glycol chain lengths are synthesized and their performances are measured first at the molecular level, and then at the device level in a Mg redox flow battery using a Mg foil as the anode, the polymer solution as the catholyte and a porous membrane as the separator. The flow battery delivers a voltage of 1.8 V, a maximum capacity of 475 mAh/L, an average Coulombic efficiency of 90.5%, an average voltage efficiency of 67.4%, an energy efficiency of 61.0%, and an energy density of 0.855 Wh/L. Systematic mechanistic studies are performed to understand the performance decay mechanism and possible strategies for future improvement are discussed. This work opens a new avenue for the development of energy storage technologies for grid electricity storage. [ABSTRACT FROM AUTHOR]