For complicated structural components with wider X-ray attenuation ranges, the projection information is short of single-energy computed tomography (CT) imaging because the attenuation thickness of the components along the orientation of X-ray penetration exceeds the limit of the dynamic range of the CT imaging system. Then under this circumstance, in the conventional imaging mode of fixed ray energy the phenomenon of overexposure and underexposure easily occurs. The whole structure information cannot be obtained, and the projection information is seriously lacking, hence it will affect the quality of CT reconstruction. This paper proposes a CT imaging method with varying energy based on logarithm demodulation.#br#For the incomplete projection due to the limited dynamic range, we collect images at various rotation angles, as in standard CT; also, at each angle we collect a series of images at different energies and fuse them into a single high dynamic range (HDR) image. Based on this HDR image, the conventional CT reconstruction methods can get the full construction information. However, the CT quality is poor, because of noise amplification in the fusion process of X-ray image sequences which are gathered during varying the X-ray energy. To solve this problem, this paper proposes to use logarithm transformation to reduce the dynamic range for the varying energy image sequences. This can change the weight coefficients' access in the projection sequences to suppress the noise. Also in the transformation sequences, we can also use the fusion method, which is based on image gray consistency, to compute the weighting coefficient, to obtain the HDR projection, because the logarithm transformation does not change the image structure, and the overlap area between image sequences is definite. Finally we use the conventional CT reconstruction algorithm to make the CT imaging with the complicated structural components.#br#An accompanying experiment with a complicated instrument demonstrates that the new method can extend the dynamic range of X-ray imaging system and provide a complete representation of the internal structure of the complicated structural components as compared with the conventional CT imaging method. So, it will be of important significance and may be applied to the potential system, so as to improve the detecting sensitivity of the system, and make the high-quality reconstruction about complex products.