We report the first operation of a widely-tunable 8-period undulator at terahertz (THz) frequencies in the Tsinghua University beamline. We observed the coherent undulator radiation from sub-picosecond electron bunches of 30MeV. The measured radiation curve shows clearly that the radiation energy is proportional to the charge square, and the THz frequency can be changed from 0.4 THz to 10 THz with narrow-band spectrums. Our results demonstrate a high power and tunable coherent THz source, which could be useful for many applications in the future.