It is an object of the present invention to provide an epoxy resin composition in which a ratio of the time between the beginning of injection and the vitrification of the epoxy resin composition to the time during which a state of liquid having such a viscosity that the epoxy resin composition can be injected is held after the beginning of injection is small, and a material in which a resin cured product has less-coloring and the appearance and the surface smoothness of the fiber-reinforced composite materials are excellent in order to enable to mold fiber-reinforced composite materials having high fiber volume fraction (Vf) and excellent mechanical properties or fiber-reinforced composite materials having a large size in a short time. The above problem can be achieved by an epoxy resin composition for a fiber-reinforced composite material comprising an epoxy resin, an acid anhydride curing agent and an organic phosphorus compound, wherein the organic phosphorus compound is contained in an amount of 0.2 to 2% by weight in terms of a phosphorus atom contained amount with respect to the sum of the epoxy resin composition, an amount of a nitrogen atom containing compound contained in the epoxy resin composition is 0 to 0.5% by weight in terms of a nitrogen atom contained amount with respect to the sum of the epoxy resin composition, and an amount of a compound having a polymerizable unsaturated group contained in the epoxy resin composition is 0 to 5% by weight with respect to the sum of the epoxy resin composition.