In this study, the molecular dynamics simulation of the shear flow of lyotropic liquid crystals which consist of spherical solvent molecules and rod-like solute molecules, have been performed using the Gay-Berne potential for rod-rod molecular interactions, the Lennard-Jones potential for sphere-sphere molecular interactions, and the extended Gay-Berne potential for rod-sphere molecular interactions. The equilibrium molecular configuration is chosen to be an initial condition. Under the shear flow, the rod-like molecules tend to align along flow direction, and the orientation order parameter tends to be higher than that for the equilibrium state. On the other hand, the rearrangements of the molecular configurations, such as the separation of domains of the spherical molecules, are found under certain conditions of the shear rate and the temperature.