We have proposed and demonstrated a new broadband terahertz (THz) wave detector using a superconducting tunnel junction (STJ) fabricated on LiNbO₃, LiTaO₃, and sapphire substrates. These substrates have relatively high absorption efficiency for THz waves, and we have expected that incident THz waves from substrate side are absorbed and that generate many THz phonons which break Cooper pairs in the base superconductor electrode of the STJ. Using a frequency-tunable THz pulse source in 1–2THz, we have confirmed that the current signal corresponding to the THz input was observed. In addition, we found two current components with different timescales for the first time. We interpret that the slow component corresponds to phonons absorbed with the substrate and that the fast one corresponds to the directly absorbed photons with the superconductor electrode of the STJs.