The geometrical-topological approach based on the Voronoi partition theory has been applied in a high-throughput search for new potential potassium solid electrolytes. After screening the Inorganic Crystal Structure Database (release 2017/2), we have selected 374 ternary and quaternary potassium- and oxygen containing compounds possessing one-, two- or three-periodic K+-ion migration maps (143, 92, and 139 compounds, respectively). Out of them, 280 compounds have not been mentioned in the literature as K+-ion conductors. We evaluated the migration energies for 18 selected compounds by the nudged elastic band method within the density functional theory (DFT) approach, and found the energies varying in a wide range (0.064-0.838 eV) and confirming the results of the geometrical topological approach. The combination of the fast geometrical-topological approach and precise DFT modeling is proved promising for prediction of ion conductivity in crystalline solids.