Rechargeable aqueous batteries are promising devices for large-scale energy-storage applications because of their low-cost, inherent safety, and environmental friendliness. Among them, aqueous ammonium-ion (NH$_4$$^+$) batteries (AAIB) are currently emerging owing to the fast diffusion kinetics of NH$_4$$^+$. Nevertheless, it is still a challenge to obtain stable AAIB with relatively high output potential, considering the instability of many electrode materials in an aqueous environment. Herein, a cell based on a concentrated (5.8 m) aqueous (NH$_4$)$_2$SO$_4$ electrolyte, ammonium copper hexacyanoferrate (N-CuHCF) as the positive electrode (cathode), and 3,4,9,10-perylene-bis(dicarboximide) (PTCDI) as the negative electrode (anode) is reported. The solvation structure, electrochemical properties, as well as the electrode–electrolyte interface and interphase are systematically investigated by the combination of theoretical and experimental methods. The results indicate a remarkable cycling performance of the low-cost rocking-chair AAIB, which offers a capacity retention of ≈72% after 1000 cycles and an average output potential of ≈1.0 V.