We discover a pressure induced quantum phase transition from the superconducting state to the non-superconducting Kondo screened phase associated with a 2% volume collapse in CeFeAsO0.7F0.3 through measurements of high-pressure resistance, synchrotron x-ray diffraction, and x-ray absorption spectroscopy (XAS) in a diamond anvil cell. Our XAS data of Ce-L3 in CeFeAsO0.7F0.3 clearly show a spectral weight transfer from the main line to the satellite line after the transition, demonstrating the formation of the Kondo singlets under pressure in CeFeAsO1-xFx. Our results have revealed a physical picture of a pressure-induce competition between Kondo singlets and BCS singlets in the Ce-pnictide superconductors.