According to physical process of light induced drift (LID) and hyperfine structure of lithium absorbing spectrum, the Boltzmann collision equation of gas diffusion and density matrix equation of semiclassical theory are combined to gain the dynamic simulation model of LID, in which, the delay time approximation and chaotic field model are used, and hyperfine structure and redistribution of excited state are taken into account. Using the statistic method of laser line width in LID, the differential equations of distribution on base and excited states of lithium atom with different velocities is proposed with chaotic field approximation.