Facial action units (AUs) recognition becomes important for facial analysis and has been widely applied in psychological research. Existing work on AU relationship learning only considers the relationship between AUs simultaneously, and does not consider the complex co-adaptation between AUs. Co-adaptation is good, but not always good. Learning the AU relationship simultaneously will inhibit the robust features of network learning. And AU relationship learning often requires additional landmark information. To solve these problems, we propose a novel AU Drop-relationship learning inspired by dropout. The AU Drop-relationship learning constructs the AU relationship units through prior knowledge. We further design the relationship regularization module to constraint the relationship between AU pairs. We randomly drop AU relationship units during training to suppress co-adaptation, forcing the network to learn more robust features. In addition, considering that there are massive unlabeled web facial images in reality, manual labeling of AU requires experts and is particularly time-consuming. To address this problem, we propose a method composed of consistency regularization and pseudo-multi-labeling for semi-supervised AU recognition. The proposed method outperforms the state-of-the-art semi-supervised and supervised methods on two widely used AU datasets (BP4D and DISFA).