The phonon dispersions of Nd(1.86)Ce(0.14)CuO(4+delta) along the [xi,0,0] direction have been determined by inelastic x-ray scattering. Compared to the undoped parent compound, the two highest longitudinal phonon branches, associated with the Cu-O bond stretching and out-of-plane oxygen vibration, are shifted to lower energies. Moreover, an anomalous softening of the bond-stretching band is observed at about q = (0.2,0,0). These signatures provide evidence for strong electron-phonon coupling in this electron-doped high-temperature superconductor.