In this paper, a significantly efficient time-domain algorithm is presented to analyze a transmission line, loaded by a nonlinear component and driven by an arbitrary modulated signal. The proposed method provides the envelope of the solution and removes the redundancy of the calculations. The efficiency of this method is achieved in two major steps. First, an unconditionally stable algorithm for the nonlinear circuit is introduced; The derived equations are generated based on the finite-difference time-domain technique and the results are confirmed by those of the Leapfrog method. As the circuit is excited by a modulated signal, decreasing the computational time by using the unconditionally stable algorithm alone, is not practical. Therefore, in the second step, a new time-domain approach is presented and utilized simultaneously, based on separating the high and low frequency behavior of the modulated signal, which enables the advantage of unconditionally stable algorithm effectively. The accuracy of the presented method is confirmed by the Leapfrog algorithm. The comparisons from the given examples indicate that almost 99.97% of the CPU time is decreased by using the proposed method.