In this work, we present a novel convolutional neural network (CNN) enabled Moiré artifacts reduction framework for the three contrast mechanism images, i.e., the absorption image, the differential phase contrast (DPC) image, and the dark-field (DF) image, obtained from an x-ray Talbot-Lau phase contrast imaging system. By mathematically model the various potential non-ideal factors that may cause Moiré artifacts as a random fluctuation of the phase stepping position, rigorous theoretical analyses show that the Moiré artifacts on absorption images may have similar distribution frequency as of the detected phase stepping Moiré diffraction fringes, whereas, their periods on DPC and DF images may be doubled. Upon these theoretical findings, training dataset for the three different contrast mechanisms are synthesized properly using natural images. Afterwards, the three datasets are trained independently by the same modified auto-encoder type CNN. Both numerical simulations and experimental studies are performed to validate the performance of this newly developed Moiré artifacts reduction method. Results show that the CNN is able to reduce residual Moiré artifacts efficiently. With the improved signal accuracy, as a result, the radiation dose efficiency of the Talbot-Lau interferometry imaging system can be greatly enhanced.