Dynamics of quantum correlation of two atoms going through a cavity one after another are investigated by means of numerical analysis method. Effects of the initial atom states and the Fock state and the atomic movement on entanglement and quantum discord and a comparison of entanglement and quantum discord are analyzed. The results show that the initial atom state can change the time evolution of entanglement and quantum discord, the increase of Fock state number can make the entanglement and quantum discord from periodic evolution to nonperiodic evolution. The nozero of the number of Fock state can lead to entanglement sudden death and nonzero quantum discord. Atomic movement can make the entanglement and quantum discord from nonperiodic evolution to periodic evolution, and can make the period shorter and it is found that the increase of the field model structure parameter can increase the entanglement and quantum discord. In some cases, the evolution law of entanglement and quantum discord are nearly same.