Contrast-enhanced computed tomography (CECT) helps enhance the visibility for tumor imaging. When a high-Z contrast agent interacts with X-rays across its K-edge, X-ray photoelectric absorption would experience a sudden increment, resulting in a significant difference of the X-ray transmission intensity between the left and right energy windows of the K-edge. Using photon-counting detectors, the X-ray intensity data in the left and right windows of the K-edge can be measured simultaneously. The differential information of the two kinds of intensity data reflects the contrast-agent concentration distribution. K-edge differences between various matters allow opportunities for the identification of contrast agents in biomedical applications. In this paper, a general radon transform is established to link the contrast-agent concentration to X-ray intensity measurement data. An iterative algorithm is proposed to reconstruct a contrast-agent distribution and tissue attenuation background simultaneously. Comprehensive numerical simulations are performed to demonstrate the merits of the proposed method over the existing K-edge imaging methods. Our results show that the proposed method accurately quantifies a distribution of a contrast agent, optimizing the contrast-to-noise ratio at a high dose efficiency.