The quantum discord of a two-qubit one-dimonsional Heisenberg XXZ spinchain in thermal equilibrium depends on the temperature T, when subjected to different magnetic fields, with B1 and B2 acting separately on the qubit, is studied in this paper. Four cases are considered here: (1) B1=B2 = 0 (without magnetic field); (2) B1≠0,B2=0 (only one qubit in magnetic field); (3) B1=B2 (homogeneous magnetic field); (4) B1=-B2 (inhomogeneous magnetic field). The similarities and difference between quantum discord and quantum entanglement are calculated and discussed in detail. Results show that the quantum discord is more robust than quantum entanglement against temperature, and the effect of inhomogeneous magnetic field is preferable for the quantum communications and quantum information processing, as compared with the effect of homogeneous magnetic field.