We model the nucleation and motion of defects in the liquid crystal display device with inhomogeneous surface by using fast Q-tensor method, which can calculate scalar order parameter S and nucleation of the defect in the liquid crystal director field. In order to model the defect, homeotropic aligned liquid crystal cell with step inhomogeneous electrode which has a height of $1{mu}m$ is used. From the simulation, we can observe the nucleation and line of the defect from surface inhomogeneity and the experiment is performed for confirmation.