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/m 2, the production method comprising the following steps -: 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; a matrix resin composition impregnating step for obtaining a prepreg precursor by impregnating a reinforcing fiber assembly being 250 - 2,000 g/m 2 in weight with the matrix resin composition; and a surface viscosity increasing step of obtaining a prepreg in which viscosity of the matrix resin composition is increased more in a superficial part than in a central part, by letting the polymerization initiator present in the superficial part of the prepreg precursor generate a radical, while not letting the polymerization initiator present in the central part generate a radical, wherein the superficial part is a region more on the outside than the fibers closest to a superficial layer, the central part is a region at a depth of at least 40 %, with respect to the thickness of the prepreg precursor being 100 %, from the surface of the prepreg precursor, the matrix resin composition used for impregnation in the step has a viscosity of 12 Pa·s to 3,000 Pa·s at 30°C, and a means for letting the polymerization initiator generate a radical in the above described step is the following method (3-i): (3-i) a method of irradiating the prepreg precursor with an energy wave selected from a group consisting of: ultraviolet; infrared; visible light; and electron beam, with an incident intensity no greater than such an incident intensity that transmittance becomes 0 % at a depth of 40 % from a surface of the prepreg precursor with respect to a thickness of the prepreg precursor being 100 %. 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; a matrix resin composition impregnating step for obtaining a prepreg precursor by impregnating a reinforcing fiber assembly being 250 - 2,000 g/m 2 in weight with the matrix resin composition; and a surface viscosity increasing step of obtaining a prepreg in which viscosity of the matrix resin composition is increased more in a superficial part than in a central part, by letting the polymerization initiator present in the superficial part of the prepreg precursor generate a radical, while not letting the polymerization initiator present in the central part generate a radical, wherein