The dispersion relations and the reflectionless conditions are obtained by the Maxwell’s curl equations in a uniaxial anisotropic medium and the phase-matching. Using the shift operator finite difference time domain （SO-FDTD） method and the transform relationship of frequency domain to time domain （jω replaced by /t）, an FDTD absorbing boundary condition for three kinds of general dispersive media model, i.e. the Debye model, Lorentz model and Drude model, is given. The characteristics of our absorbing boundary condition are tested. The computed results illustrated the generality and the feasibility of the scheme.