After researching the forming principle of X-ray beam hardening and analyzing the usual methods of beam hardening correction, a beam hardening correction model was established, in which the independent variable was the projection gray, and so the computing difficulties in beam hardening correction can be reduced. By considering the advantage and disadvantage of fitting beam hardening curve to polynomial, a new expression method of the subsection beam hardening curves based on polynomial was proposed. In the method, the beam hardening data were fitted firstly to a polynomial curve which traverses the coordinate origin, then whether the got polynomial curve surged in the fore-part or back-part of the fitting range was judged based on the polynomial curvature change. If the polynomial fitting curve surged, the power function curve was applied to replace the surging parts of the polynomial curve, and the C1 continuity was ensured at the joints of the segment curves. The experimental results of computed tomography (CT) simulation show that the method is well stable in the beam hardening correction for the ideal CT images and CT images with added noises, and can mostly remove the beam hardening artifact at the same time.