An H-L Consistency based beam hardening correction method of CT with polychromatic x-ray tube spectrum has been proposed recently. To identify its effectiveness, a comparison research is completed in the paper between this method and water phantom experiment correction used in current CT devices. For reason of isolating irrelevant influence, the simulated projection data of Forbild head phantom based on physics of medical x-ray imaging are used to evaluate correction effects. Firstly, a virtual circular fan beam CT with known parameters (tube spectrum, added filter, mechanical parameters, etc.) is constructed. Secondly, a simulated isotropic water phantom is used to generate normal correction polynomial in current CT device (called normal correction). Thirdly, for the projection data of given CT phantom, sole-polynomial and bi-polynomial correction based on H-L Consistency, and normal water phantom correction are applied respectively. Fourthly, all the corrected projection data are reconstructed with the same FBP algorithm. The correction effects of beam hardening artifact are compared between those three applied correction methods, especially the differences of correction effects in different slices. Simulation experiments show that the bi-polynomial method can achieve the best effect, although it costs more computation resource, and the H-L Consistency based method exhibit accordant correction effect for different slices, whereas the normal correction cannot adapt all slices equally.