The direct process of spin-lattice relaxation in the ground state of ruby of low concentration is calculated at low temperature. The nonradiative transition probabilities within the four ground sub-levels are calculated by aid of second-order wave functions obtained in the strong-field coupling scheme. Under the measured condition of impulse saturation at θ=90°, the spin-lattice relaxation time at 1.4°K is obtained by solving the rate equations. The calculated result conforms satisfactorily to the experimental data given by Pace et al.