A new class of fully 4-dimensional image reconstruction algorithm for cardiac CT was developed. The proposed method is an iterative algorithm that alternates two methods, motion estimation (ME) method and motion compensated reconstruction (MCR) method. The ME method estimates the cardiac MVF using elastic image registration between the reference phase and other phases. The motion of heart was modeled by the linear combination of cubic B-spline basis function. The sum of squared difference and spatial and temporal regularization terms were chosen as the cost function, which is minimized by a nested conjugate gradient method. The MCR method (Schafer's method) reconstructs cardiac images using the MVF estimated by the ME method. The reconstructed images will be fed to ME in the next iteration. The ME and MCR were performed alternately till convergence was achieved. Accuracy of the proposed method was evaluated using 3 patient data acquired by a 64-slice CT scanner. The heart rates of the patients ranged between 52 and 88 beats-per-minute. The motion artifacts were significantly decreased by the proposed method, and the degree of improvement increased as the iteration progressed.