An accelerator test facility, t-ACTS, was established at Research Center for Electron Photon Science, Tohoku University, in which an intense coherent terahertz (THz) radiation is generated from an extremely short electron bunch. Velocity bunching scheme in a traveling-wave accelerating structure is employed to produce the short electron bunch. 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 developed to produce intense coherent THz radiation. Properties of the radiation from the THz undulator such as an electric field of the radiation, the spectrum and, angular distribution were numerically investigated based on the parameters of short electron bunch and the THz undulator. By optimization of bunch compression, it is possible to extract a coherent radiation of fundamental mode excluding higher-order modes. The detail of the numerical studies for the coherent undulator radiation and a preparation of beam experiment are reported.