We investigated the dynamic behaviors of a three qubits system coupled to an XY spin chain with Dzyaloshinsky-Moriya (DM) interaction by calculating the global quantum discord.The effect of system-environment couplings and the DM interaction on the quantum discord are given.The results indicated that the effect of the DM interaction on the decay of discord is not remarkable in the weak-coupling region.However,in the strong-coupling region,t...