Topological insulators (TIs) are interesting quantum matters that have a narrow bandgap for bulk and a Dirac-cone-like conducting surface state (SS). The recent discovered second Dirac surface state (SS) and bulk bands (BBs) located similar to 1.5 eV above the first SS are important for optical coupling in TIs. Here, we report on the time-domain measurements of THz radiation generated from TIs n-type Cu0.02Bi2Se3 and p-type Bi2Te3 single crystals by ultrafast optical pulse excitation. The observed polarity-reversal of the THz pulse originated from transient current is unusual, and cannot be reconciled with the photo-Dember effect. The second SS and BBs are found to be indispensable for the explanation of the unusual phenomenon. Thanks to the existence of the second SS and BBs, TIs manifest an effective wide band gap in THz generation. The present study demonstrates that time-domain THz spectroscopy provide rich information of the optical coupling and the electronic structure of TIs.