We have observed that C-60(+) ions isolated in cryogenic matrices show distinct near-IR photoluminescence upon excitation in the near-IR range. By contrast, UV photoexcitation does not lead to measurable luminescence. Near-IR G(60)(+) photoluminescence is a one-photon process. The emission is mainly concentrated in one band and corresponds to (2)A(1u) -> E-2(1g) relaxation. We present experimental data for the Stokes shift, power, and temperature dependencies as well as the quantum efficiency of the photoluminescence. Our findings may be relevant for astronomy, considering recent unequivocal assignment of five diffuse interstellar bands to near-IR absorption bands of G(60)(+).