Abstract: This paper presents two kinds of absorbing boundaries for the two-dimensional (2-D) Leapfrog Alternating Direction Implicit Finite-Difference Time-Domain (Leapfrog ADI-FDTD) method—Mur boundary and CPML absorbing boundary condition. Leapfrog ADI-FDTD had unconditional stability and all the iterative equations were implicit. However, the electric and magnetic field components for the 2-D leapfrog ADI-FDTD method were updated implicitly as well as explicitly, absorbing boundary condition for difference components might keep diversity. Updating equations of CPML are presented in the paper according to its derived theory and compared with first-order Mur absorbing boundary condition. What's more, the reflection error of free space was used to represent absorbing ability of absorbing boundary condition.