<p>A composition which comprises (A) an epoxy-containing vinyl ester resin having 0.8 to 0.3 equivalent of epoxy groups and 0.2 to 0.7 equivalent of ethylenically unsaturated groups in the molecule, (B) a radical-polymerizable monomer, (C) a curing agent, and (D) carbon fiber impregnated with (d) 0.5 to 5 % by mass of a sizing agent consisting of a vinyl ester resin obtained by the addition reaction of an epoxy resin with an ethylenically unsaturated carboxylic acid; and carbon fiber -reinforced resin composite materials produced by curing the composition.</p>