We study the superconducting-gap anisotropy of the Γ-centered hole Fermi surface in optimally doped FeTe(0.6)Se(0.4) (T(c)=14.5 K), using laser-excited angle-resolved photoemission spectroscopy. We observe sharp superconducting (SC) coherence peaks at T=2.5 K. In contrast to earlier angle-resolved photoemission spectroscopy studies but consistent with thermodynamic results, the momentum dependence shows a cos(4φ) modulation of the SC-gap anisotropy. The observed SC-gap anisotropy strongly indicates that the pairing interaction is not a conventional phonon-mediated isotropic one. Instead, the results suggest the importance of second-nearest-neighbor electronic interactions between the iron sites in the framework of s(±)-wave superconductivity.