The continuous exploration of advanced electrode materials is of remarkable significance to revolutionize next-generation high-performance energy storage devices towards a green future. Benefiting from their electrochemically active sites and abundant redox centers, bimetallic selenides with desirable nanostructures recently have emerged as promising electrode alternatives for battery-supercapacitor hybrid (BSH) devices which demonstrate enormous potential in bridging the gap between electrochemical properties with high power densities (supercapacitors) and energy densities (batteries). Herein, employing the hydrothermal approach with solid Ni-Co spheres as precursors followed by the selenization process, selenide-rich bimetallic selenide spheres with a core-shell nanostructure were rationally designed and synthesized for use as the cathode electrode in superior BSH devices. The as-obtained (NiCo)9Se8/(NiCo)0.85Se (Ni-Co-Se) exhibits a high specific capacity of 164.44 mA h g-1 at a current density of 1 A g-1 with 85.72% capacity retention even after 5000 cycles at a current density of as high as 8 A g-1, suggesting its great promise in practical applications for BSH devices. By integrating activated carbon as the anode with the as-obtained bimetallic selenides as the cathode, an alkaline aqueous BSH device is fabricated and delivers a high energy density of 37.54 W h kg-1 at a high power density of 842.7 W kg-1. It is found that the excellent electrochemical performances can be ascribed to facile ion and electron transport pathways, high electrical conductivity and reliable structural robustness of the prepared selenides. Moreover, the synthetic strategy presented in this paper opens up an avenue to guide the synthesis of various anion doped bimetallic compounds towards high-performance energy conversion and storage devices.