Sleep staging is an important task that enables sleep quality assessment and disorder diagnosis. Due to dependency on manually labeled data, many researches have turned from supervised approaches to self-supervised learning (SSL) for sleep staging. While existing SSL methods have made significant progress in terms of its comparable performance to supervised methods, there are still some limitations. Contrastive learning could potentially lead to false negative pair assignments in sleep signal data. Moreover, existing data augmentation techniques directly modify the original signal data, making it likely to lose important information. To mitigate these issues, we propose Self-Supervised Learning with Attention-aided Positive Pairs (SSLAPP). Instead of the contrastive learning, SSLAPP carefully draws high-quality positive pairs and exploits them in representation learning. Here, we propose attention-based latent signal augmentation, which plays a key role by capturing important features without losing valuable signal information. Experimental results show that our proposed method achieves state-of-the-art performance in sleep stage classification with limited labeled data. The code is available at: https://github.com/DILAB-HYU/SSLAPP