Based on a broad-sense modified “one for two” idea, the elaborately designed 3,4,9,10-perylene-tetracarboxylic-dianhydride (PTCDA)-based metal-organic frameworks (MOFs) are employed as the precursor for fabrication of both a battery-type (porous NiCo2S4) and a capacitive (N-doped carbon) electrode to form battery-supercapacitor hybrid cell (BSC). By inhering the topology of the precursor NiCo-PTCDA-MOFs, the derived NiCo2S4 is endowed with abundant effective pores. Meanwhile, combining the rigid planar structure of PTCDA and linked with N-containing 2,6-diaaino-anthraquinone (DAAQ) into polyquinoneimine (PQI) as a ligand, the Zn-PQI-MOFs-derived N-doped carbon shows high surface area. By coupling the porous NiCo2S4 with the N-doped carbon, the BSC demonstrates 234 C g−1 at the current density of 1 A g−1, remaining 56.4% of the initial specific capacity from 1 to 20 A g−1. A high energy density of 51.98 W h kg−1 at the power density of 0.8 kW kg−1 surpasses those for the two symmetric cells made from similar electrodes. This work significantly extends the application of ligands with large conjugated structures in MOFs, which is essentially a new direction of MOFs-derived materials for energy storage.