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This paper describes a fast finite-element time-domain (FETD) method using the iterative leapfrog mixed (ILM)-FETD method. To circumvent a time step size limitation of an existing leapfrog mixed (LM)-FETD method, which adopts a mixed E-B finite element formulation and a leapfrog scheme, we introduce an iterative procedure of the leapfrog scheme. Because iterative solutions of the ILM-FETD method converge to the solutions obtained by an unconditionally stable FETD method, the proposed approach can use a relatively larger time step size than the LM-FETD method. Some numerical results show that the ILM-FETD method is about 4 times faster than the existing method with appropriate accuracy.