Numerical simulation based on the modified time-dependent Ginzburg-Landau (TDGL) model has been performed on the domain growth and related rheological properties of binary mixtures under oscillatory shear. The simulation results reveal that the domain growth is anisotropic and depends on the quench depth. It is found that, in the deep quench case, the disclike domain with the normal parallel to the velocity gradient direction is observed, while in the shallow quench case, the rodlike domain with rod axis aligned along the flow direction is observed. The scattering functions for different light incident directions are calculated and suggest that the undulated rodlike morphology is formed in the shallow quench case. This undulated rodlike morphology shows the anomalous rheological response. A plausible interpretation for the anomalous rheological property is proposed based on the deformation of the undulated rodlike morphology under oscillatory shear.