The property of quantum nonlocality in the atom-field coupling system via degenerate Raman processes with cavity damping is investigated. It is found that if the cavity dissipation is very weak, the atom-field state can exhibit quantum nonlocality periodically. The rapidity of the loss of the quantum nonlocality depends on the amplitude of the initial coherent state and the cavity damping constant. The stronger the field is and the larger the damping constant could be, the more rapidly the nonlocality decreases.