Provided are: an epoxy resin composition for fiber-reinforced composite materials, which has a good balance between storage stability and fast curing properties at high levels; a prepreg; and an epoxy resin composition which exhibits excellent mechanical characteristics as a fiber-reinforced composite material. A resin composition which contains an epoxy resin, dicyandiamide, an imidazole compound and an acidic compound, while satisfying the following conditions (a)-(c): (d) The time until the heat flow rate reaches the peak top after the epoxy resin composition reaches 100° C. is 25 minutes or less as measured by a differential scanning calorimeter at an isothermal temperature of 100° C. in a nitrogen gas stream. (e) The time until the heat flow rate reaches the peak top after the epoxy resin composition reaches 60° C. is 15 hours or more as measured by a differential scanning calorimeter at an isothermal temperature of 60° C. in a nitrogen gas stream. (f) The ratio of the number of epoxy groups to the number of imidazole rings in the epoxy resin composition is from 25 to 90 (inclusive).