Nano-structuring methods are actively applied to solid oxide fuel cell electrodes to reduce the operating temperature while preserving a high electro-catalytic activity. The unique nanoscale microstructure is vital to electrochemical performance, yet not well quantified in three dimensions. Here, with a multi-stage recovering principle of distance correlation functions, the three-dimensional microstructures of La0.8Sr0.2MnO3-delta nano-particles infiltrated porous Y0.16Zr0.84O2-delta electrodes are reconstructed with a dimension of 1024 x 1024 x 1024 voxels at a resolution of 7.5 nm from one two-dimensional micrograph. The key geometric characteristics, such as tortuosity factors, active surface/interface areas and three-phase boundary length, are calculated from the reconstructed three-dimensional microstructures at various loadings of La0.8Sr0.2MnO3-delta. Combining with the analysis of distribution of relaxation times, the active three-phase boundary length is shown to be the main factor governing the electrode impedance, and is related quantitatively to the electrochemical process at high frequency. The accuracy of capturing nanoscale features is validated by the focused ion beam sectioning dataset of a Ni-Y0.16Zr0.84O2-delta electrode at nanoscale resolution. This work provides a promising strategy for reconstructing three-dimensional heterogeneous nanostructures from one super-resolution two-dimensional micrograph, and demonstrates a quantitative approach for uncovering processing-structure-property relationships of nano-structured electrodes and beyond.