X-ray two-photon absorption (TPA) spectrum of metallic copper is measured using a free-electron laser (XFEL). The spectrum differs from that measured by the conventional one-photon absorption (OPA), and characterized by a peak below the Fermi level, which is assigned to the transition to the 3d state. The impact of the XFEL pulse on the OPA spectrum is discussed by analyzing the pulse-energy dependence, which indicates that the intrinsic TPA spectrum is measured.