By using of polarization spectrum, a laser frequency stabilization system for Cr atom lithography was designed. In order to eliminate the noise and improve the signal-to-noise ratio, a Lock-in amplifier was used. Calculation shows that the frequency discrimination signal is a purely dispersive signal. The energy sublevel distributions of Cr atom, which are important for frequency discrimination signal as the designed system would be used for Cr atom lithography, were also discussed. The nuclear magnetic torque of Cr atom is zero, which in turn has no influence on the energy level of Cr atom. Calculation shows that several other factors, such as the isotopes and the earth magnetic field, had little influence on the energy level of Cr atom, indicating that they could be ignored in the current experimental system. Some factors which will influence the line width and the linearity of the discrimination signal are also discussed.