Plane-wave ab initio calculations based on density function theory and the pseudopotential method have been used to investigate the structural properties of crystalline ammonium dinitramide (ADN) under hydrostatic compression in the pressure range 0-300 GPa. Optimization of the crystal structure has been done with full relaxation of atomic positions and lattice parameters without any symmetry constraints. The calculations were performed using periodic boundary conditions in all three directions. Changes in the electronic bands, charge distributions, and geometric parameters of the crystal have been computed as functions of pressure. We find that the ADN crystal maintains its monoclinic structure with P2(1)/c symmetry for pressures up to 10 GPa, where there is a transition to a P (1) over bar triclinic symmetry. The crystalline phase transition involves reorientation of the ammonium ions relative to the dinitramide ions as well as additional rotations of the NO2 groups relative to the N-N-N plane of dinitramide ions.