Although ZnMn2O4 is widely studied as Li-ion battery anodes, it remains a challenge to tailor suitable microstructures of the oxide for supercapacitor applications. Carbon-coated ZnMn2O4 (C@ZMO) nanocrystallites showing high-performance pseudocapacitor behaviours in neutral aqueous electrolyte are for the first time successfully synthesised via a novel solution combustion process using polyethylene glycol as a multifunctional microstructure-directing agent. Controlling the molecular weight and amount of the polymer in the combustion solution enables the formation of highly-crystalline C@ZMO having substantially higher, by more than 5 folds, specific surface areas with mesoporous structures and conformal carbon coating via the one-pot synthesis process. The resulting C@ZMO supercapacitor electrodes in Na2SO4(aq) electrolyte exhibit ideal capacitive behaviours with specific capacitances up to 150 F g−1 and cycle stability showing no capacitance fade after 10,000 cycles at 60% of full capacity and >99% Coulombic efficiency. This study not only illustrates a new powerful synthesis route capable of producing conductive mesoporous crystalline oxide-based nanomaterials for energy storage applications but also reveals a new class of high-performance pseudocapacitive materials for neutral aqueous electrolytes.