Excellent in adhesion and long-term storage stability of the carbon fiber and the matrix resin, to provide a prepreg and carbon-fiber reinforced composite material excellent in microcrack resistance by a high toughness. The present invention is an aliphatic epoxy compound (A) and the aromatic epoxy compound sizing agent applying carbon fibers coated with a sizing agent containing (B1) the form of a fabric or braid, a thermosetting resin (D), the thermoplastic resin (F) and a latent curing agent (G) prepreg formed by impregnating a thermosetting resin composition containing the surface of said sizing agent coating the carbon fibers, C _1s, as measured by X-ray photoelectron spectroscopy (a) CHx of the inner shell spectrum, C-C, the ratio of the height of the components of the binding energy attributed to C = C, and the height of the components of the binding energy attributed to the (b) C-O (a) / (b) it is characterized by a predetermined range.