Respiratory motion may change SUVmax and SUVpeak in PET images and compromise target definition and treatment response assessment in radiation therapy. While 4D imaging techniques may help address these issues, the time required for 4D data acquisition, image reconstruction and administrative costs keep 3D PET imaging staying as the mainstream in clinical practice. The purpose of this study is to explore the potential of using 4DCT information to remove motion-induced errors in 3D PET/CT images. A novel iterative image-to-image (III) reconstruction algorithm was developed. Specifically, a motion-blurred PET image was considered as a weighted average of PET images acquired at different respiration phases. PET images at each phase were assumed to be deformed from a virtual reference image. Image-intensity-based B-Spline registrations were performed on 4DCT from the end-inhale to the other phases. Resultant deformation maps were used to establish a set of composition equations between the virtual reference image and the blurred PET image. A maximum likelihood estimation maximization (MLEM) algorithm was used to solve these equations. The solution of these equations was smoothed by minimizing total gradient variations before generating the virtual reference image. A 10-phase 4D dataset with the resolution of 3.64×3.64×3.24 for PET and1.37×1.37×2.15 for CT was acquired from a lung cancer patient and used to benchmark the computed results. Different from previous studies, the III-reconstruction was performed in the image space, so there is no any tracking device or sorting operation required during the PET image acquisition. For the blurred PET, III-reconstructed PET and PET0 (which is the 4D-PET at the end-inhale phase), their relative SUVpeak are 10.2, 12.7 and 12.8, and SUVmax are 9.2, 12.5 and 13.1. With PET0 taken as the baseline, the III-reconstruction reduced the motion-induced error from 20.3% to 0.8% for SUVpeak, and from 29.8% to 4.6% for SUVmax. The mean SUV difference between the III-reconstructed PET and PET0 was 1.8% in the tumor region, and 13.2% over the whole image domain. Large differences between the two PET images were located mainly in the chest wall where ribs were mis-registered about 6 mm due to discontinuous motion between the ribs and lungs. The III-reconstruction algorithm was also applied to the 4DCT image. Image contrast ratios for the blurred 3DCT, III-reconstructed CT, and CT0 are 1.8, 3.7 and 4.0, respectively. The III-reconstruction method can be used to correct motion-induced errors in SUVmax and SUVpeak and improve image contrasts in free-breathing PET and CT images. This method does not require sorting projection data, thereby reducing financing cost and clinical burden. Further investigation of this reconstruction method is warranted.