Provided are a composite material that adequately obtains the effect of carbon nanotubes, a prepreg in which the composite material is used, a carbon-fiber-reinforced molded article having greater resistance to the progression of the interlayer peeling crack, and a method for manufacturing the composite material. A composite material includes a carbon fiber bundle in which a plurality of continuous carbon fibers are arranged, carbon nanotubes adhering to respective surfaces of the carbon fibers, and a plurality of fixing resin parts partly fixing the carbon nanotubes on the surfaces of the carbon fibers, where the fixing resin parts cover 7% or more and 30% or less of the surfaces of the carbon fibers to which the carbon nanotubes adhere.