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 (CoSex, 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 CoSex rather than crystalline CoSe2. 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 CoSex-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%), CoSe2.7-AHP achieves a balance between capacity and cycling stability. Amorphous CoSe2.7-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 CoSex-AHP undergoes reversible redox of Co2+/3+↔Co0 and Sen 2‒↔Se2‒. The present study demonstrates amorphous polyselenides with cationic-anionic redox activities is as a feasible strategy to construct high-capacity cathode materials for RMBs.