Two-dimensional (2D) metal–organic frameworks (MOFs) have been a worldwide research interest due to their potential application in supercapacitors. Herein, a cobalt-based layered MOF ([Co2(μ-SO4)(Hppza)2(H2O)3]n, namely, SEU-1; H2ppza = 3-(pyridin-4-yl)-1H-pyrazole-5-carboxylic acid) has been synthesized via a one-step solvothermal method. Single X-ray diffraction analysis shows that the SEU-1 exhibits a (3,3,4)-connected 2D structure with a Schläfli symbol of (62·8)(63)(64·8·10). Variable-temperature magnetic susceptibility data display that antiferromagnetic interactions between two CoII ions exist in SEU-1. The supercapacitive performance has been evaluated in the three-electrode system. Its maximum specific capacitance is 145.5 F g−1 at 1 A g−1, along with the specific capacitance retention of 92.7% at the current density of 5 A g−1 after 6000 cycles in 3 M KOH solution. These results demonstrate that SEU-1 is a good candidate for electrode material for electrochemical energy storage.