Metal organic frameworks (MOFs) have been considered as one of the most promising electrode materials for electrochemical capacitors due to their large specific surface area and abundant pore structure. Herein, we report a Co-MOF electrode with a vertical-standing 2D parallelogram-like nanoarray structure on a Ni foam substrate via a one-step solvothermal method. The as-prepared Co-MOF on a Ni foam electrode delivered a high area-specific capacitance of 582.0 mC cm-2 at a current density of 2 mA cm-2 and a good performance rate of 350.0 mC cm-2 at 50 mA cm-2. Moreover, an asymmetric electrochemical capacitor (AEC) device (Co-MOF on Ni foam//AC) was assembled by using the as-prepared Co-MOF on a Ni foam as the cathode and a active carbon-coated Ni foam as the anode to achieve a maximum energy density of 0.082 mW cm-2 at a power density of 0.8 mW cm-2, which still maintained 0.065 mW cm-2 at a high power density of 11.94 mW cm-2. Meanwhile, our assembled device exhibited an excellent cycling stability with a capacitance retention of nearly 100% after 1000 cycles. Therefore, this work provides a simple method to prepare MOF-based material for the application of energy storage and conversion.