The present invention discloses: a composition comprising (A) an epoxy group-containing vinyl ester resin having, in the molecule, 0.8 to 0.3 equivalent of epoxy group and 0.2 to 0.7 equivalent of an ethylenically unsaturated group, (B) a radical-polymerizable monomer, (C) a curing agent, and (D) a carbon fiber impregnated with 0.5 to 5% by mass of (d) a vinyl ester resin as a sizing agent, obtained by an addition reaction of an epoxy resin and an ethylenically unsaturated carboxylic acid, and a carbon fiber-reinforced resin composite material produced by curing the above composition.