This is the first report of single-cycle terahertz (THz)-wave pulse generation with a wide band (over 6 THz) and a high dynamic range (over 70 dB) using an organic nonlinear optical crystal, 4-dimethylamino-N′-methyl-4′-stilbazolium tosylate (DAST), and the prism-coupled Cherenkov phase-matching method. The prism-coupled approach allowed the use of a DAST crystal as a Cherenkov-type emitter for reduced light absorption by the crystal, resulting in the generation of single- and half-cycle THz pulse shapes, which were detected using dipole and bow-tie antennas, respectively. The resulting THz pulse generation is suitable for various THz-wave application technologies, such as tomography.