Layered potassium cobaltate K0.36CoO2 has been successfully synthesized from KOH fluxes at 480℃. The K0.36CoO2 sample can be oxidized and intercalated with water by treatment in KMnO4 and K2S2O8 solutions. K0.12CoO2·0.8H2O and K0.16CoO·0.6H2O have been obtained after the KMnO4 and K2S2O8 treatment, respectively. The diffraction peaks of K0.12CoO2·0.8H2O and K0.16CoO2·0.6H2O can be well indexed by a hexagonal cell similar to the monolayer hydrate NaxCoO2·yH2O. After dehydration, the major phases have an orthorhombic structure similar to Na0.5CoO2 and show semiconductor behavior. Both K0.12CoO2·0.8H2O and K0.16CoO2·0.6H2O are primari paramagnetic and show metallic behavior. K0.16CoO2·0.6H2O has a spin-glass-like transition or other magnetic fluctuations around 56K. The spin-glass-like transition or the regions of magnetic phase separation are reduced in K0.12CoO2·0.8H2O due to the increasing of the intercalated water. We also discussed similarities and differences between the structural and physical properties of KxCoO2 and NaxCoO2.