The dependence of the nuclear spin-lattice relaxation time T1 on the strength of an applied magnetic field has been calculated for the α phase of solid nitrogen. The relaxation is thought to be primarily quadrupolar relaxation due to the librating nitrogen molecules. At all but the lowest temperatures the dominant relaxation processes are expected to be the anharmonic Raman and first-order Raman processes. On the assumption that a spin temperature exists for the spins on a particular sublattice J of the α-phase structure, these relaxation processes yield an expression for T1(0)T1J(H-->) which is almost independent of temperature. In the special case when the magnetic field is along a  direction, T1J(H-->) is the same for all four sublattices and T1(0)T1(H) rises to a value of about 1.5 in large magnetic fields. For other directions of H--> and for a polycrystalline sample a range of values of T1(H) is expected.