Energy quantization is considered for an electrone moving inside a Bloch domain wall in a metallic ferromagnet. We show that the effective potential for electrons moving along these domain walls is parabolic as a function of the coordinate perpendicular to the doman walls. Therefore the quantum ehergy levels E_n for these electrons are equidistant, i.e., E_n=nhΩ. We demonstrate that the effective frequency Ω is much higher than the frequency Ω₀ of the cyclotron motion of an electron in a domain.