Transfer learning-based methods for the remaining useful life (RUL) prediction of bearings require accessing target domains at model training stages, which limit the practical value as many real-world cases are with totally unseen domains. In addition, the life-stage domain shift within time-series data is rarely considered in tackling the unseen domain problems. To this end, this study is motivated to develop a novel network model possessing the awareness of the life-stage domain shift information to overcome challenges induced by unseen working conditions and intradomain distribution shifts. The development of the resulting model, the life-stage domain aware network, is composed of two parts. In the first part, an unsupervised learning scheme is proposed for handling the life-stage division via sensing intradomain distribution shifts. In the second part, a domain aware network tailored for life-stages is developed to build a shared domain-invariant latent space through the subdomain alignment at each stage. A preliminary theoretical analysis is conducted to show that invariant features can be learned under the proposed learning framework. The superiority of the RUL prediction model developed by the proposed method is validated through comparisons with the state-of-the-art methods on different bearing datasets.