A compact racetrack-type 700 MeV storage ring (HiSOR) has been constructed at Hiroshima Synchrotron Radiation Center (HSRC). As the ring was planned for synchrotron radiation research on science and technology using VUV to X-rays up to 5 keV with limited size and cost, the ring was designed (i) to realize a high magnetic field (2.7 T) using conventional dipole magnets for higher critical energy, and (ii) to include two straight sections for insertion devices. A linear undulator (25-300 eV) and a new-type helical/linear undulator were installed at the two straight sections. The latter undulator consists of upper and lower jaws, as in a planar undulator; each jaw consists of one fixed magnet array at the centre and two magnet arrays on both sides. By longitudinal displacement of the side magnet arrays, the phase between the vertical and horizontal magnetic fields, and therefore the polarization (right- or left-circular, elliptical, linear) can be selected. The helical/linear undulator gives almost perfect circular polarization at 4-40 eV in the helical configuration without changing the phase of the magnet arrays, as well as linearly polarized light at 3-300 eV in the linear configuration.