While many superionic conductors for light alkali metal ions (Li+ or Na+) have been developed based on ceramics and metal-organic composite materials, fast ion conduction of larger K+ ions in ambient conditions has long been a challenging target because of the large ionic radius of K+ ion. Recently, our research group reported a unique supramolecular framework of the nanometer-sized spherical metal complex (K-NCIS), which shows excellent K+ conduction of 13 mS/cm at room temperature. Although the presence of many solvated water molecules in the crystals accelerated the K+ conductivity in K-NCIS, the mobility of K+ was not frozen even below 0 ºC owing to the anomalous behavior of water molecules filled in the crystal lattice. The high transport number (t) of K+ for K-NCIS was proven by the NMR spectroscopy and ion-diffusion experiment in the solid-state. An ongoing study on constructing all-solid-state K+ batteries using K-NCIS as solid-electrolyte will also be described.