A series of layered CeO1-xFxFeAs compounds with x=0 to 0.20 are synthesized by the solid state reaction method. Similar to the LaOFeAs, the pure CeOFeAs shows a strong resistivity anomaly near 145 K, which was ascribed to the spin-density-wave instability. F doping suppresses this instability and leads to the superconducting ground state. Most surprisingly, the superconducting transition temperature could reach as high as 41 K. Such a high T_{c} strongly challenges the classic BCS theory based on the electron-phonon interaction. The closeness of the superconducting phase to the spin-density-wave instability suggests that the magnetic fluctuation plays a key role in the superconducting pairing mechanism. The study also reveals that the Ce 4f electrons form local moments and are ordered antiferromagnetically below 4 K, which could coexist with superconductivity.