User modeling is critical for personalization. Existing methods usually train user models from task-specific labeled data, which may be insufficient. In fact, there are usually abundant unlabeled user behavior data that encode rich universal user information, and pre-training user models on them can empower user modeling in many downstream tasks. In this paper, we propose a user model pre-training method named UserBERT to learn universal user models on unlabeled user behavior data with two contrastive self-supervision tasks. The first one is masked behavior prediction and discrimination, aiming to model the contexts of user behaviors. The second one is behavior sequence matching, aiming to capture user interest stable in different periods. Besides, we propose a medium-hard negative sampling framework to select informative negative samples for better contrastive pre-training. Extensive experiments validate the effectiveness of UserBERT in user model pre-training.