The spin-lattice relaxation (SLR) of the photoexcited tripler states in fullerene C-60 crystal is investigated at low temperatures and high magnetic fields. The mixing of the translational and rotational motions of the molecules (TRM relaxation mechanism) is chosen as the major phenomenon, leading to the coupling of the spin system with acoustic vibrations, The general expressions of the SLR rates for the direct one-phonon processes are obtained, The results of calculation are in accordance with available experimental data.