Abstract: The THz radiation generated by the vacuum electron device is often the ring-based or linac-based source. The generation of relativistic, sub-picosecond electron pulses allows the direct production of high-power, coherent THz radiation by passing the electron beam through an undulator. This provides a reliable and easily tunable powerful source of THz radiation for scientific applications. In this paper, the generation and observation of coherent THz undulator radiation from a femtosecond accelerator facility was reported. The accelerator facility consisted of an S-band thermionic cathode RF-gun, an alpha magnet and a SLAC-type accelerating tube, which could provide the electron bunches with energy of 20-30 MeV and bunch length of 100-300 fs. The undulator was an Apple-II type undulator, which could operate in various linear, elliptical or circular modes when the two rows at one diagonal moved along the longitudinal direction. To measure the frequency spectrum of the THz radiation, a modified Michelson interferometer was employed. The experiment setups were described and experiment results were given.