We have studied production of the very short-bunch electron beam to generate intense coherent THz radiation. The coherent synchrotron radiation spectrum is proportional to the bunch form factor, and in order to obtain large form factor enough to generated intense coherent THz radiation, very short bunches (< 100 fs) must be produced. The beam from the thermionic RF-gun is introduced into the bunch compression system consist of an alpha magnet and a linac. The alpha magnet is used in order to rotate the longitudinal phase space. The bunch compression is done in the linac employing velocity bunching. The beam is injected on near the zero-cross phase of the RF field in the linac, and then the beam phase slips toward the crest. The particle distribution in the longitudinal phase space and the beam phase with respect to RF field at the entrance of the linac are optimized so as to produce the minimum bunch length. In addition to space charge effect, the transfer matrix of the alpha magnet has coupling terms in the 6-dimensional phase space, analytical evaluation of the beam dynamics is very difficult. Then, we used a numerical simulation based on the GPT code . Consequently the bunch length of 60 fs has been obtained for a bunch charge of 20 pC. We discuss the bunch compression scheme in this article.