We show that in ͑TMTSF͒ 2 ClO 4 the field-induced spin-density wave ͑FISDW͒ with negative quantum number ͑N =−2͒ of the nesting vector is stabilized in some region in the parameters of magnetic field and the strength of the anion potential, which corresponds to the very recently observed phase diagram of ͑TMTSF͒ 2 ClO 4 in the parameter plane of magnetic field vs cooling rate by Matsunaga et al. ͓J. Phys. IV 131, 269 ͑2005͔͒. The spin-density wave is induced by the magnetic field in the quasi-one-dimensional conductors such as ͑TMTSF͒ 2 PF 6 and ͑TMTSF͒ 2 ClO 4 . The wave vector of the FISDW is quantized and the Hall conductivity is quantized corresponding to the quantum number ͑N͒ of the wave vector. In ͑TMTSF͒ 2 ClO 4 , the ordering of the anion ClO 4 makes the periodic potential, which has been known to drastically affect the FISDW. We study the instability to the FISDW by taking the eigenstates in the magnetic field numerically, with the periodic potential being treated nonperturbatively. We obtain the phase diagram of the quantum number N for FISDW in the quasi-one-dimensional systems in the parameter plane of magnetic field and the strength of the periodic potential, which can be controlled by the cooling rate.