In this paper, the stealth characteristics of the coated missile are studied. Through analyzing the relationship between Debye equation of and filed variable in time-domain, the shifting operator is applied to deriving the formulas of finite-difference time domain for dispersive medium, and the Maxwell's equations are modified to make the FDTD expression independent of the dispersive medium. The frequency-dependent expressions of FDTD in the dispersive medium are given. The comparison of the simulating results of this method to the results of literatures shows that the method adopted in this paper is effective in calculating the scattering characteristics of dispersive medium and that plasma plays a distinct role in decreasing RCS. The simulation results of missile coated with plasma are given. The effect of parameters selecting on stealthy characteristics is analyzed.