A test accelerator as a coherent terahertz source (t-ACTS) has been under development at Tohoku University, in which an intense coherent terahertz (THz) radiation generated by an extremely short electron bunch . Velocity bunching scheme in a traveling accelerating structure is employed to generate femtosecond electron bunches . Spatial and temporal coherent radiation in THz region can be produced by the electron bunches with small transverse emittance. A long-period undulator, which has 25 periods with a period length of 10 cm and a peak magnetic field of 0.41 T, has been also developed and installed to provide intense coherent THz undulator radiation. By optimizing the bunch length, we found that it is possible to generate a coherent undulator radiation that contains only the fundamental wave from numerical studies. Beam experiment was performed to generate and observe the coherent undulator radiation from extremely short electron bunches. Coherent undulator radiation from 2.6 to 3.6 THz was demonstrated. The preliminary results of the experiment will be reported in this paper. mentally confirmed the production of short electron bunch by measuring the bunch length using a streak camera and analysing spectrum of coherent transition radiation in THz region [4-6]. Generation of coherent undulator radiation is studied and demonstrated at t-ACTS.