The spin-lattice relaxation of donor electrons in silicon is investigated. The relaxation rate is calculated using the adiabatic approximation, in which the electronic wave function is determined instantaneously according to the Hamiltonian which is perturbed by the lattice deformation. The rate thus obtained found to be equal to that obtained when we take a simple product of the electronic and the lattice wave functions as a starting wave function and take the electron-lattice interaction as a perturbation. We considered the modulation of the spin-orbit coupling due to the lattice vibration as well as deformation of the donor wave function due to the external magnetic field. When we consider one-phonon process, the relaxation rate was found to be proportional to H4T, as is observed. The absolute magnitude of the rate also agrees with the observation in orders of magnitude.