This paper is devoted to investigation of luminescence and some electric properties of C-60 single crystal and their connection with X-traps model. Luminescence properties for C-60 single crystal, the temperature dependence of the luminescence spectra and decay kinetics were measured for wide range of excitation energies. At low temperatures the emission spectra with well resolved structure were detected. Opposite to the case of C-60 films, the single crystal shape of the luminescence spectra also change with temperature. This behavior can be described in terms of X-trap model as proposed in [1]. The luminescence kinetics under 36 eV excitation as a function of temperature was investigated in nanosecond range. At temperature T < 300 K, the decay curve is non-exponential and it can be fitted formally by two exponents with characteristic times in the 1-100 ns range. We suppose the explanation of this relaxation behavior requires more particular information about electron-hole recombination dynamics which can be affected by X-traps. Following X-traps concept we present preliminary results of thermostimulated currents spectroscopy experiments. It reveals the availability of two thermorelaxation processes in C-60 single crystal and therefore indeed the presence at least of two types of traps for charges in this crystals.