In order to obtain high magnetic fields in a short period undulator, superconductive undulators have been actively investigated in recent years. In this paper, however, we propose a new approach, the cryogenic permanent magnet undulator (CPMU) design, using permanent magnets at the cryogenic temperature of liquid nitrogen or higher. This cryogenic scheme can be easily adapted to currently existing in-vacuum undulators and it improves the magnetic field performance by 30%--50%. Unlike superconductive undulators operating around the liquid helium temperature, there is no big technological difficulty such as the thermal budget problem. In addition, existing field correction techniques are applicable to the CPMUs. Since there is no quench in the CPMUs, the operation of the CPMUs has the same reliability as conventional permanent magnet undulators.