In this letter, a further study for the alternating-direction implicit (ADI) scheme used in the mixed E and B finite-element time-domain (FETD) method is performed. Based on a direct discretization of the first-order coupled Maxwell curl equations and employed Whitney form basis functions to expand the electric field and the magnetic field, an efficient algorithm for implementing ADI scheme in FETD method is presented. Compared to the Crank-Nicolson (CN) scheme used in the FETD method, theoretical analysis and numerical results demonstrate that the ADI-FETD method has no splitting error, the accuracy of the two methods is the same, and the ADI-FETD method is exactly a two-step scheme for CN-FETD method.Index Terms-Alternating-direction implicit (ADI) scheme, Crank-Nicolson (CN) scheme, finite-element time-domain (FETD) method.