The g-shifts in spin-Peierls (SP) and magnetic (M) phases of the inorganic spin-Peierls material CuGeO3 have been observed by submillimeter wave ESR. The temperature dependence of the g-shifts from U phase to SP or M phase showed a continuous change. Since such g-shifts were also observed in the organic spin-Peierls material, for example TTF-AuBDT, such g-shifts can be considered the universal phenomena due to the lattice distortion in the spin-peierls materials. But, in the case of CuGeO3, the g-shifts are so large that we cannot explain them in the framework of the point charge model with considering the continuous lattice distortion.