The nontime-step-splitting leapfrog alternating-direction-implicit finite-difference-time domain (ADI-FDTD) method is extended to plasma calculation based on Laplace Transform Principle. It is called Current-Density-Laplace-Transform (CDLT) leapfrog ADI-FDTD method. The corresponding formulations for isotropic plasma are derived. In order to verify the effectiveness of this method, the reflection and transmission coefficients of plasma plate are calculated. The numerical results show that the precision and efficiency of the proposed unconditionally stable method are both higher than that of the conventional explicit FDTD methods.