Provided is a prepreg which comprises the following constituent elements (A) to (C), constituent element (A) having been disposed on one or both surfaces of a layer comprising constituent element (B) and constituent element (C): (A) nonwoven fabric comprising a thermoplastic elastomer and/or a polyolefin which each has a tand at 10 C of 0.06 or more in a viscoelasticity examination and which each is incompatible with the constituent element (B); (B) a first epoxy resin composition; and (C) reinforcing fibers. The present invention further provides a fiber-reinforced composite material which has excellent rigidity, strength, and vibration-damping properties. The prepreg is suitable for use in obtaining this composite material. Furthermore provided is a process for producing the prepreg.