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As biometric authentication systems are popularly used in various mobile devices, e.g., smart-phones and tablets, face anti-spoofing methods have been actively developed for the high-level security. However, most previous approaches still suffer from diverse types of spoofing attacks, which are hardly covered by the limited number of training datasets, and thus they often show the poor accuracy when unseen samples are given for the test. To address this problem, a novel method for face anti-spoofing is proposed based on one-class (i.e., live face only) learning with the live correlation loss. Specifically, encoder-decoder networks are firstly trained with only live faces to extract latent features, which have an ability to compactly represent various live facial properties in the embedding space and produce the spoofing cues, which are simply obtained by subtracting the original RGB image and the generated one. After that, such features are fed into the proposed feature correlation network (FCN) so that weights of FCN learn to compute ''liveness'' of given features under the guidance of the live correlation loss. It is noteworthy that the proposed method only requires live facial images for training the model, which are easier to obtain than fake ones, and thus the generality power for resolving the problem of face anti-spoofing can be expected to be improved. Experimental results on various benchmark datasets demonstrate the efficiency and robustness of the proposed method.