We investigate the dynamics of quantum discord for a two-qubit system coupled to a spin chain with three-site interaction in the weak-coupling region.For the case of the initial two-qubit pure state,the decay of quantum discord can be delayed in a special interval of the three-site coupling strength.In the absence of the transverse field,with the increase of three-site interaction,quantum discord tends to be stabler.For the case of the initial mixed state,the increase of quantum discord is delayed in the special interval of three-site interaction.In addition,a sudden transition between classical and quantum decoherence is aiso observed,with the transition time determined by the three-site interaction and degree of anisotropy.