A method for producing a fiber-reinforced composite material plate by heating and pressurizing a prepreg for a molding time of 15 minutes or less, at a molding temperature of at least 120.degree. C. and a molding pressure of at least 10 kg/cm.sup.2. The prepreg is prepared from a reinforcing fiber and an epoxy resin composition. The epoxy resin composition features: an epoxy resin; an amine compound having at least one sulfur atom in the molecule thereof and/or a reaction product of the epoxy resin and the amine compound having at least one sulfur atom in the molecule thereof; a urea compound; and a dicyandiamide. The contents of the sulfur atom and the urea compound in the epoxy resin composition are respectively 0.2 to 7% by mass and 1 to 15% by mass.