For myocardial perfusion CT exams, beam hardening (BH) artifacts may degrade the accuracy of myocardial perfusion defect detection. Meanwhile, cardiac motion may make BH process inconsistent, which makes conventional BH correction (BHC) methods ineffective. The aims of this study were to assess the severity of BH artifacts and motion artifacts and propose a projection-based iterative BHC method which has a potential to handle the motion-induced inconsistency better than conventional methods. In this study, four sets of forward projection data were first acquired using both cylindrical phantoms and cardiac images as objects: (1) with monochromatic x-rays without motion; (2) with polychromatic x-rays without motion; (3) with monochromatic x-rays with motion; and (4) with polychromatic x-rays with motion. From each dataset, images were reconstructed using filtered back projection; for datasets 2 and 4, one of the following BHC methods was also performed: (A) no BHC; (B) BHC that concerns water only; and (C) BHC that takes both water and iodine into account, which is an iterative method we developed in this work. Biases of images were quantified by the mean absolute difference (MAD). The MAD of images with BH artifacts alone (dataset 2, without BHC) was comparable or larger than that of images with motion artifacts alone (dataset 3): In the study of cardiac image, BH artifacts account for over 80% of the total artifacts. The use of BHC was effective: with dataset 4, MAD values were 170 HU with no BHC, 54 HU with water BHC, and 42 HU with the proposed BHC. Qualitative improvements in image quality were also noticeable in reconstructed images.