An object is to provide a graphite-copper composite electrode material that is capable of reducing electrode wear to a practically usable level and to provide an electrical discharge machining electrode using the material. A graphite-copper composite electrode material includes a substrate comprising a graphite material and having pores, and copper impregnated in the pores of the substrate, the electrode material having an electrical resistivity of 2.5 μΩm or less, preferably 1.5 μΩm or less, more preferably 1.0 μΩm or less. It is desirable that the substrate comprising the graphite material have an anisotropy ratio of 1.2 or less. It is desirable that an impregnation rate φ of the copper in the electrode material is 13% or greater. It is desirable that the substrate comprising the graphite material have a bulk density of from 1.40 Mg/m3 to 1.85 Mg/m3.