Even though the X-ray Computed Tomography (CT) scan is considered suitable for fast imaging, motion-artifact-free cardiac imaging is still an important issue, because the gantry rotation speed is not fast enough compared with the heart motion. To obtain a heart image with less motion artifacts, a motion estimation (ME) and motion compensation (MC) approach is usually adopted. In this paper, we propose an ME/MC algorithm that can estimate a nonlinear heart motion model from a sinogram with a rotation angle of less than 360 degrees. In this algorithm, we first assume the heartmotion to be nonrigid but linear, and thereby estimate an initial 4-D motion vector field (MVF) during a half rotation by using conjugate partial angle reconstructed images, as in our previous ME/MC algorithm. We then refine the MVF to determine a more accurate nonlinear MVF by maximizing the information potential of a motion-compensated image. Finally, MC is performed by incorporating the determined MVF into the image reconstruction process, and a time-resolved heart image is obtained. By using a numerical phantom, a physical cardiac phantom, and an animal data set, we demonstrate that the proposed algorithm can noticeably improve the image quality by reducing motion artifacts throughout the image.