In X-ray CT imaging, a basic assumption is that an imaging object has no motion. However, a patient who has a mental or behavior disease cannot hold his/her head still during the scan, and thereby severe motion artifacts occur in the reconstructed image. In order to reduce the artifacts due to the 3D rigid motion of the patient’s head, we propose a FDK-based motion compensated reconstruction algorithm. The algorithm is based on the motion parameter estimation by maximizing the quality of motion compensated reconstructed image. We evaluate the validity of the proposed motion estimation and compensation algorithm by using a numerical phantom with motion.