To achieve high electrochemical performance of polyoxometalates (POMs)-based materials, introducing POMs to crystalline supramolecular structures via hydrogen bonding interactions represents a potential strategy. Herein, a new semi-rigid pyrazole-amide-derived bis(pyridyl) ligand N,N'-bis(3-pyridinamide)-1-hydropyrazole (3-Hdpyp) was designed due to the abundant hydrogen bond sites of amide group, as well as the multiple N-donor sites, which was used to assemble with the Keggin-type [PMo12O40]3− (PMo12) anion and cobalt under solvothermal condition. A new 2D sandwich-like supramolecular network [Co2(3-dpyp)2(H2O)2][HPMo12O40] (1) was synthesized and structurally characterized. The PMo12 anions are fixed between the 1D metal–organic chains [Co2(3-dpyp)2(H2O)2]n2n+via hydrogen bonding interaction. Complex 1 shows excellent specific capacitances 1062.5F g−1 at the current density of 1 A g−1. After 1000 cycles, it can maintain 90.0% of the capacitance retention. Meanwhile, complex 1 represents an excellent amperometric sensor for measurement of Cr(VI) with low detection limit of 0.22 µM. The excellent electrochemical performance can be attributed the discrete 2D sandwich-like structures, which can improve the active area of POMs and conductivity of the network.