Disclosed are polyacrylonitrile carbon fibers excellent in substrate strength and adhesion to matrix resin wherein average nitrogen content in the whole carbon fibers which is measured by elementary analysis is 0.5-4.5% by weight and average nitrogen concentration (N/C atom number ratio) in the whole carbon fibers which is measured by elementary analysis and surface silicon concentration (Si.sub.2p /C.sub.1s atom number ratio), surface nitrogen concentration (N.sub.1s /C.sub.1s atom number ratio) and surface oxygen concentration (O.sub.1s /C.sub.1s atom number ratio) which are measured by X-ray photoelectron spectroscopy satisfy the following formulas:0.ltoreq.Si.sub.2p /C.sub.1s .ltoreq.0.020.67 N/C+0.08.ltoreq.O.sub.1s /C.sub.1s -2 Si.sub.2p /C.sub.1s .ltoreq.0.40.ltoreq.N.sub.1s /C.sub.1s -N/C.ltoreq.0.04and method for producing the carbon fibers.