Metal-organic frameworks are a complex of metal nodes and organic ligands that have attracted widespread interest in technological applications owing to their diverse characteristics. Bi-linker MOFs can prove to be more conductive and efficient than the mono-linker MOFs, however, they have been investigated less often. In this current study two distinct organic ligands i.e., 1,2,4,5-benzene-tetra-carboxylic acid and pyridine-3,5-dicarboxylic acid were used to synthesize a bi-linker nickel MOF. The obtained Ni-P-H MOF having a unique construction was examined for its structural, morphological, and electrochemical properties. To the best of our knowledge, for the first time its potential use was specifically explored as a component in hybrid supercapacitors, as it has not been previously reported for such applications. In standard three-electrode assembly, the electrochemical properties of the Ni-P-H MOF were examined, followed by the fabrication of a Ni-P-H MOF hybrid supercapacitor with activated carbon. This hybridization results in a device with both high energy and power density, making it suitable for a variety of practical applications. To further understand the behavior of this hybrid supercapacitor, a semi-empirical technique was implemented employing Dunn's model. This model allows for the extraction of regression parameters and the quantification of the diffusive/capacitive contributions of the two-cell assembly. Overall, the combination of Ni-PMA-H2pdc MOF//activated carbon in a hybrid supercapacitor holds great potential for advancements in energy storage technology.