This paper presents a numerical procedure to calculate the time-domain response of thin-wire antennas over Debye media. The method is based in an expansion of the electric-field integral-equation in the time-domain (EFIE-TD), which accounts for the Debye media by using a reflection-coefficient approach. Resulting extended integral equation is subsequently solved by the method of moments. Numerical examples including Debye soils show not only the accuracy of the method but also a higher computational efficiency in comparison with other hybrid numerical techniques.