Rechargeable magnesium batteries (RMBs) are a promising energy-storage technology with low cost and high reliability, while the lack of high-performance cathodes is impeding the development. Herein, a series of amorphous cobalt polyselenides (CoSe x , x>2) is synthesized with the assistance of organic amino-terminal hyperbranched polymer (AHP) additive and investigated as cathodes for RMBs. The coordination of cobalt cations with the amino groups of AHP leads to the formation of amorphous CoSe x rather than crystalline CoSe 2 . The amorphous structure is favorable for magnesium-storage reaction kinetics, and the polyselenide anions provide extra capacities besides the redox of cobalt cations. Moreover, the organic AHP molecules retained in CoSe x -AHP provide an elastic matrix to accommodate the volume change of conversion reaction. With a moderate x value (2.73) and appropriate AHP content (11.58%), CoSe 2.7 -AHP achieves a balance between capacity and cycling stability. Amorphous CoSe 2.7 -AHP provides high capacities of 246.6 and 94 mAh g ‒1 , respectively, at 50 and 2000 A g ‒1 , as well as a capacity retention rate of 68.5% after 300 cycles. The mechanism study demonstrates CoSe x -AHP undergoes reversible redox of Co 2+/3+ ↔Co 0 and Se n 2‒ ↔Se 2‒ . The present study demonstrates amorphous polyselenides with cationic-anionic redox activities is as a feasible strategy to construct high-capacity cathode materials for RMBs.