The present invention relates to a method of producing a prepreg, in which a matrix resin is applied to a reinforcing fiber sheet, where the sheet can continuously run without clogging due to generated fuzz, even at a high running speed, and where the sheet can be efficiently impregnated with the matrix resin. The prepreg is produced by a method which includes a step of allowing a reinforcing fiber sheet to pass horizontally or slantingly through the inside of a coating section storing a matrix resin to apply the matrix resin to the reinforcing fiber sheet, where the coating section includes a liquid pool and a narrowed section which are in communication with each other, where the liquid pool has a portion whose cross-sectional area decreases continuously along a running direction of the reinforcing fiber sheet, and wherein the narrowed section has a slit-like cross-section and has a smaller cross-sectional area than the largest cross-sectional area of the liquid pool.