Face aging is the task aiming to translate the faces in input images to designated ages. To simplify the problem, previous methods have limited themselves only able to produce discrete age groups, each of which consists of ten years. Consequently, the exact ages of the translated results are unknown and it is unable to obtain the faces of different ages within groups. To this end, we propose the continuous face aging generative adversarial networks (CFA-GAN). Specifically, to make the continuous aging feasible, we propose to decompose image features into two orthogonal features: the identity and the age basis features. Moreover, we introduce the novel loss function for identity preservation which maximizes the cosine similarity between the original and the generated identity basis features. With the qualitative and quantitative evaluations on MORPH, we demonstrate the realistic and continuous aging ability of our model, validating its superiority against existing models. To the best of our knowledge, this work is the first attempt to handle continuous target ages.