Designing and preparing dual-functional Dawson-type polyoxometalate-based metal–organic framework (POMOF) energy storage materials is challenging. Here, the Dawson-type POMOF nanomaterial with the molecular formula CoK4[P2W18O62]@Co3(btc)2 (abbreviated as {P2W18}@Co-BTC, H3btc = 1,3,5-benzylcarboxylic acid) was prepared using a solid-phase grinding method. XRD, SEM, TEM et al. analyses prove that this nanomaterial has a core–shell structure of Co-BTC wrapping around the {P2W18}. In the three-electrode system, it was found that {P2W18}@Co-BTC has the best supercapacitance performance, with a specific capacitance of 490.7 F g−1 (1 A g−1) and good stability, compared to nanomaterials synthesized with different feedstock ratios and two precursors. In the symmetrical double-electrode system, both the power density (800.00 W kg−1) and the energy density (11.36 Wh kg−1) are greater. In addition, as the electrode material for the H2O2 sensor, {P2W18}@Co-BTC also exhibits a better H2O2-sensing performance, such as a wide linear range (1.9 μM–1.67 mM), low detection limit (0.633 μM), high selectivity, stability (92.4%) and high recovery for the detection of H2O2 in human serum samples. This study provides a new strategy for the development of Dawson-type POMOF nanomaterial compounds.