An electrical discharge machining electrode wire includes a core including a copper or a copper alloy, and a covering layer covering a periphery of the core and including a zinc. The covering layer includes an inner layer including a γ-phase of copper-zinc based alloy and covering the periphery of the core, and an outer layer including an ε-phase of copper-zinc based alloy and covering a periphery of the inner layer. An x-ray diffraction intensity of (0001) of the ε-phase is more than twice an x-ray diffraction intensity of (332) of the γ-phase.