Abstract: Oxidizing treatment of carbon fibers under specific conditions provides carbon fibers having oxygen concentration (O.sub.1S /C.sub.1S atom number ratio) in the surface part of the carbon fibers of 0.05 to 0.30 as measured by X-ray photoelectron spectroscopy, coefficients of water-extractable fraction of up to 2.0, and coefficients of tow spread of at least 1.times.10.sup.-3. These carbon fibers are excellent in adhesion to various matrix resins and when mixed as reinforcements with matrix resins, provide composite materials superior especially in impact resistance. The thus obtained composite materials are useful for aircraft, automobiles, and general industrial materials.