In this study, we propose to remove Moiré image artifact induced by system instabilities in grating-based x-ray interferometry imaging using convolutional neural network (CNN) technique. This method reduces Moiré image artifact in image-domain via a learned image post-processing procedure, rather than developing signal retrieval optimization algorithms to minimize the inconsistencies between acquired phase stepping data and assumed signal model. To achieve this aim, we suggested to train the CNN network using dataset synthesized from both natural images and experimentally acquired Moiré artifact-only images. In particular, a novel approach is developed to generate a large number of various high quality Moiré artifact-only images from finite groups of experimental phase stepping data. Both numerical and experimental results demonstrate that the developed CNN method is able to effectively remove the undesired Moiré image artifact. As a result, the image quality of a practical grating-based x-ray interferometry system can be greatly improved.