We explore the phase diagram, structures, electron properties, and potential superconductivity of the K-P system at pressures of up to 200 GPa through unbiased structure searching techniques and first-principles calculations. Five stable chemical stoichiometries (K4P, K3P, K2P, KP, and KP2) have been theoretically predicted. In particular, P-2 units or P-chains are uncovered in K2P, KP, and KP2 compounds with the existence of covalent bonds by analyzing the electron localization functions. And the Bader analysis demonstrates that charges transfer from K atoms to P atoms. Electron-phonon calculations show that the T-c of metallic I4/mmm-KP2 is 22.01 K at 5 GPa. The investigating of the K P system is in favor of understanding the crystal structures and corresponding properties of potassium phosphides, which also give a strong motivation to search and design new superconductor materials in other phosphides.