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In this paper, a generalized absorbing boundary condition (Z-ABCs) is constructed in the Z-transform domain. Based on Z-ABCs, some well-known ABCs, such as the Mur's ABC, the dispersive boundary condition, Zhao and Litva's ABC, Liao's ABC, etc. can be easily deduced. Besides, it can also result in some new ABCs. Recurrence formulas for the coefficients of Z-ABCs are presented, and the stability and numerical dispersive characteristics are discussed in detail. In order to validate the Z-ABCs, the finite-difference time-domain method is applied to the analysis of transmission lines, integrated filters, patch antennas, and scattering problems.