Metal–organic frameworks have received increasing attention as promising electrode materials in supercapacitors. In this study, we have successfully synthesized a novel accordion-like Ni-MOF superstructure ([Ni3(OH)2(C8H4O4)2(H2O)4]·2H2O), for the first time, and used it as an electrode material for supercapacitors. The supercapacitors with the novel electrode exhibited excellent electrochemical performance. For example, the accordion-like Ni-MOF electrode showed specific capacitances of 988 and 823 F g−1 at current densities of 1.4 and 7.0 A g−1, respectively, while maintaining outstanding cycling stability (capacitance retention of 96.5% after 5000 cycles at a current density of 1.4 A g−1). More importantly, the accordion-like Ni-MOF and activated carbons were assembled into a high-performance flexible solid-state asymmetric supercapacitor with a specific capacitance of 230 mF cm−2 at a current density of 1.0 mA cm−2. The cycle test showed that the device can offer 92.8% capacity of the initial capacitance at 5.0 mA cm−2 after 5000 cycles with little decay. The maximum energy density of the device can achieve 4.18 mW h cm−3 and the maximum power density can also achieve 231.2 mW cm−3.