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A coherent THz light source was built in Shanghai Institute of Nuclear Research (SINR), Chinese Academy of Science. A variable elliptically polarized undulator with Apple-II structure was designed to produce the linear polarized as well as various elliptical polarized THz radiations. The structure of the undulator corresponds to four standard Halbach-type magnet rows which consist of two pairs of planar permanent magnet rows above and below the electron orbit plane. The two rows at one diagonal can move along the longitudinal direction to provide the various polarization modes. The period and the gap are 100mm and 36 mm respectively and the number of period is five. This paper describes the magnet design, the force calculation and the stress analysis of the undulator. The magnetic fields are optimized for the horizontal linear polarization mode and the circular polarization mode.