The present invention relates to a method for producing a prepreg which contains reinforcing fibers and a matrix resin composition with the weight per square meter of the reinforcing fibers being 250-2,000 g/m2. The production method comprises the following steps (1)-(3): (1) a matrix resin composition blending step for obtaining a matrix resin composition by mixing an epoxy resin, a radically polymerizable unsaturated compound, an epoxy resin curing agent and a polymerization initiator that generates radicals, in said step the content of the radically polymerizable unsaturated compound relative to 100% by mass of the total of the epoxy resin and the radically polymerizable unsaturated compound being 10-25% by mass; (2) a matrix resin composition impregnating step; and (3) a surface viscosity increasing step.