The dynamics of quantum discord (QD) is investigated in the two-qubit Ising system in an inhomogeneous magnetic field with the Dzialoshinskii-Moriya (DM) interaction. The system is initially prepared in the Werner state, and the effects of the DM interaction, degree of inhomogeneous magnetic field and purity of the initial state on QD and entanglement in the evolution process are analyzed in detail. By comparison, it is found that both the quantum discord and entanglement take similar behaviors to a large extent, and QD does not vanish in the finite time, but the phenomenon of entanglement sudden death (ESD) appears during the evolution process. This difference shows that the quantum discord is more practical than the entanglement to evaluate the quantum correlation. These effects also indicate that one can control the quantum discord of the system by some exterior conditions.