A method of producing a prepreg, comprising the steps of: allowing a reinforcing fiber sheet to pass substantially vertically downward through the inside of a coating section storing a matrix resin to apply said matrix resin to said reinforcing fiber sheet to obtain a matrix resin-impregnated reinforcing fiber sheet; and heating said matrix resin-impregnated reinforcing fiber sheet in a noncontact manner; wherein said coating section comprises a liquid pool and a narrowed section which are in communication with each other, wherein said liquid pool has a portion whose cross-sectional area decreases continuously along a running direction of said reinforcing fiber sheet, and wherein said narrowed section has a slit-like cross-section and has a smaller cross-sectional area than the area of the top side of said liquid pool; wherein the noncontact heating is started within a region of 1 m from the opening of said narrowed section in the running direction of said matrix resin-impregnated reinforcing fiber sheet; wherein, assuming that the surface temperature of said matrix resin-impregnated reinforcing fiber sheet is P2 °C at the completion point of the heating and that the temperature of said matrix resin stored in the inside of said coating section is M°C, M ≤ P2; and wherein said coating section comprises, in said liquid pool, a width regulation mechanism (27a, 27b) for regulating the width of said reinforcing fiber sheet, and wherein the relationship between the width of said reinforcing fiber sheet immediately under said narrowed section and the width regulated by said width regulation mechanism (27a, 27b) at the lower end of said width regulation mechanism satisfies L 2 ≤ W + 10 mm. allowing a reinforcing fiber sheet to pass substantially vertically downward through the inside of a coating section storing a matrix resin to apply said matrix resin to said reinforcing fiber sheet to obtain a matrix resin-impregnated reinforcing fiber sheet; and heating said matrix resin-impregnated reinforcing fiber sheet in a noncontact manner; wherein said coating section comprises a liquid pool and a narrowed section which are in communication with each other, wherein said liquid pool has a portion whose cross-sectional area decreases continuously along a running direction of said reinforcing fiber sheet, and wherein said narrowed section has a slit-like cross-section and has a smaller cross-sectional area than the area of the top side of said liquid pool; wherein the noncontact heating is started within a region of 1 m from the opening of said narrowed section in the running direction of said matrix resin-impregnated reinforcing fiber sheet; wherein, assuming that the surface temperature of said matrix resin-impregnated reinforcing fiber sheet is P2 °C at the completion point of the heating and that the temperature of said matrix resin stored in the inside of said coating section is M°C, M ≤ P2; and wherein said coating section comprises, in said liquid pool, a width regulation mechanism (27a, 27b) for regulating the width of said reinforcing fiber sheet, and wherein the relationship between the width of said reinforcing fiber sheet immediately under said narrowed section and the width regulated by said width regulation mechanism (27a, 27b) at the lower end of said width regulation mechanism satisfies L 2 ≤ W + 10 mm.