Face Forgery videos have elicited critical social public concerns and various detectors have been proposed. However, fully-supervised detectors may lead to easily overfitting to specific forgery methods or videos, and existing self-supervised detectors are strict on auxiliary tasks, such as requiring audio or multi-modalities, leading to limited generalization and robustness. In this paper, we examine whether we can solve this issue by leveraging visual-only real face videos. To this end, we propose to learn the Natural Consistency representation (NACO) of real face videos in a self-supervised manner, which is inspired by the observation that fake videos struggle to maintain the natural spatiotemporal consistency even under unknown forgery methods and different perturbations. Our NACO first extracts spatial features of each frame by CNNs then integrates them into Transformer to learn the long-range spatiotemporal representation, leveraging the advantages of CNNs and Transformer on local spatial receptive field and long-term memory respectively. Furthermore, a Spatial Predictive Module (SPM) and a Temporal Contrastive Module (TCM) are introduced to enhance the natural consistency representation learning. The SPM aims to predict random masked spatial features from spatiotemporal representation, and the TCM regularizes the latent distance of spatiotemporal representation by shuffling the natural order to disturb the consistency, which could both force our NACO more sensitive to the natural spatiotemporal consistency. After the representation learning stage, a MLP head is fine-tuned to perform the usual forgery video classification task. Extensive experiments show that our method outperforms other state-of-the-art competitors with impressive generalization and robustness.