Complex microstructures of liquid-crystalline polymers in nonhomogenous shear flow are studied by element free Galerkin (EFG) method based on the micro-macro dualscale model. The dualscale model combines the orientational diffusion equation in microscale with the flow governing equations in macroscale. The EFG method which has the merits of high accuracy and good stability can ensure the reliability of the simulation results. One simple and five composite structures of liquid-crystalline polymers in nonhomogenous shear flow are predicted by studying the influences of Deborah number on microstructures of liquid-crystalline polymers in plane Poiseuille flow. It shows that the instabilities in the transition region of the composite structures can cause some defects.