The time-domain finite-element method (TDFEM) is extended to study the two-dimensional transient electromagnetic scattering from multiple targets above a rough surface in this article. The perfectly matched layer is employed as the truncation boundary of TDFEM region to absorb the outward wave scattered from the model. To introduce the incident wave, a total field boundary, which splits the whole region into total-and scatteredfield regions is built around the composite model. To model the composite scattering, the total-and scatteredfield formulas are used in these two regions, respectively. Numerical results are presented to demonstrate the accuracy, efficiency, and flexibility of the method. The results show that the proposed method is significantly superior to the time-domain integral equation method in terms of solving time.