A method is described for producing a prepreg formed by applying a matrix resin to a reinforcing fiber sheet, wherein the method can effect continuous running without clogging due to generated fuzz even at a high running speed and effect efficient impregnation of the reinforcing fiber sheet with a matrix resin. A method of producing a prepreg includes allowing a reinforcing fiber sheet to pass substantially vertically downward through the inside of a coating section storing a matrix resin to obtain a matrix resin-impregnated reinforcing fiber sheet in which the matrix resin is applied to the reinforcing fiber sheet and at least heating the matrix resin-impregnated reinforcing fiber sheet, wherein the coating section includes a liquid pool and a narrowed section which are in communication with each other, wherein the liquid pool has a portion whose cross-sectional area decreases continuously along a running direction of the reinforcing fiber sheet.