The morphology and the corresponding rheological properties of phase separating binary mixtures under shear flow are studied by computer simulation based on the modified time-dependent Ginzburg-Landau (TDGL) model. In order to investigate the hydrodynamic effect, model H in three dimensions has been used to simulate the phase separation of binary fluids under shear flow. For the sake of comparison, the simulation has also been performed based on simple binary solid model (model B). It is found that, for deep and critical quench, the domain grows faster and the domain anisotropy is lower in binary fluids due to the internal flow field induced by hydrodynamic interaction. For deep and off-critical quench, the internal flow field makes the elongated domain quickly relax to their original spherical shape before they are mutually contacted each other. Thus, it reduces the domain merging probability. It is also found that, for deep and critical quench, there are two peaks appeared in the shear viscosity as a function of shear strain at low shear rate, which agrees with the experimentally observations quite well. For shallow quenching, the broader interfaces suppress the internal flow caused by hydrodynamic interaction and thus the difference between binary solids and binary fluids is small. All these observed unique characters have been explained according to the hydrodynamic interaction and the relaxation rate of the deformed interface.