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.