The present invention relates to a method for producing a composite molded article having a flexural modulus at 150° C. of 25% or more of a flexural modulus at 23° C., including the steps of (1) placing glass fibers in a mold; (2) impregnating glass fibers with a polymerizable composition containing a cycloolefin monomer, a metathesis polymerization catalyst, a radical generator, and a compound represented by the general formula (I); (3) subjecting the above polymerizable composition with which the glass fibers are impregnated to a bulk polymerization to provide a composite molded article; and (4) demolding the composite molded article; and a composite molded article obtained by the above method. According to the method of the present invention, a composite molded article containing glass fibers, the composite molded article having excellent mechanical strength can be produced.