Magnetic junction is considered which consists of two ferromagnetic metal layers, a thin nonmagnetic spacer in between, and nonmagnetic lead. Theory is developed of a magnetization reversal due to spin injection in the junction. Spin-polarized current is perpendicular to the interfaces. One of the ferromagnetic layers has pinned spins and the other has free spins. The current breaks spin equilibrium in the free spin layer due to spin injection or extraction. The nonequilibrium spins interact with the lattice magnetic moment via the effective s-d exchange field, which is current dependent. Above a certain current density threshold, the interaction leads to a magnetization reversal. Two threshold currents are found, which are reached as the current increases or decreases, respectively, so that a current hysteresis takes place. The theoretical results are in accordance with the experiments on magnetization reversal by current in three-layer junctions Co/Cu/Co prepared in a pillar form.PACS: 75.60.Ej; 75.70.Cn.