Electrode materials with a large internal surface area, tunable pore size, efficient transport of electrons and high ion-accessibility are highly desired in the development of advanced flexible supercapacitors. Recently, transition metal sulfides with rationally designed nanostructures have attracted considerable attention as electrode materials for supercapacitors. In this study, we report the synthesis of Zn0.76Co0.24S/NiCo2S4 nanosheets grown on carbon cloth using a two-dimensional bimetallic Zn/Co zeolitic imidazolate framework (named as Zn/Co-ZIF-L) as a precursor through a simple and cost-effective chemical solution process. The ZIF-derived Zn0.76Co0.24S/NiCo2S4 electrode nanosheets deliver an ultrahigh specific capacitance of 2674 F g−1 at 1 A g−1, a superior ratio performance and cycle stability. Furthermore, the as-fabricated Zn0.76Co0.24S/NiCo2S4//AC all-solid-state asymmetric supercapacitor (ASC) achieves a maximum energy density of 48.1 Wh kg−1 as well as a power density of 837 W kg−1, and a superior cycling performance of 91% retention after 5000 cycles. The detailed electrochemical kinetic analysis demonstrates that the total capacitance of Zn0.76Co0.24S/NiCo2S4 is derived from its capacitive-effective charge storage mechanism. This ZIF-derived strategy provides a reasonable and simple way to synthesize transition metal sulfides as potential active materials for next-generation flexible supercapacitors.