Free-breathing abdomen imaging requires non-rigid motion registration of unavoidable respiratory motion in three-dimensional undersampled data sets. In this work, we introduce an image registration method based on the convolutional neural network (CNN) to obtain motion-free abdominal images throughout the respiratory cycle. Abdominal data were acquired from 10 volunteers using a 1.5 T MRI system. The respiratory signal was extracted from the central-space spokes, and the acquired data were reordered in three bins according to the corresponding breathing signal. Retrospective image reconstruction of the three near-motion free respiratory phases was performed using non-Cartesian iterative SENSE reconstruction. Then, we trained a CNN to analyse the spatial transform among the different bins. This network could generate the displacement vector field and be applied to perform registration on unseen image pairs. To demonstrate the feasibility of this registration method, we compared the performance of three different registration approaches for accurate image fusion of three bins: non-motion corrected (NMC), local affine registration method (LREG) and CNN. Visualization of coronal images indicated that LREG had caused broken blood vessels, while the vessels of the CNN were sharper and more consecutive. As shown in the sagittal view, compared to NMC and CNN, distorted and blurred liver contours were caused by LREG. At the same time, zoom-in axial images presented that the vessels were delineated more clearly by CNN than LREG. The statistical results of the signal-to-noise ratio, visual score, vessel sharpness and registration time over all volunteers were compared among the NMC, LREG and CNN approaches. The SNR indicated that the CNN acquired the best image quality (207.42 ± 96.73), which was better than NMC (116.67 ± 44.70) and LREG (187.93 ± 96.68). The image visual score agreed with SNR, marking CNN (3.85 ± 0.12) as the best, followed by LREG (3.43 ± 0.13) and NMC (2.55 ± 0.09). A vessel sharpness assessment yielded similar values between the CNN (0.81 ± 0.03) and LREG (0.80 ± 0.04), differentiating them from the NMC (0.78 ± 0.06). When compared with the LREG-based reconstruction, the CNN-based reconstruction reduces the registration time from 1 h to 1 min. Our preliminary results demonstrate the feasibility of the CNN-based approach, and this scheme outperforms the NMC- and LREG-based methods. Advances in knowledge: This method reduces the registration time from ~1 h to ~1 min, which has promising prospects for clinical use. To the best of our knowledge, this study shows the first convolutional neural network-based registration method to be applied in abdominal images.