Automated Cobb angle estimation based on X-ray images plays an important role in scoliosis diagnosis, treatment, and progression surveillance. The inadequate feature extraction and the noise in X-ray images are the main difficulties of automated Cobb angle estimation, and it is challenging to ensure that the calculated Cobb angle meets clinical requirements. To address these problems, we propose a Landmark-aware Network named LaNet with three components, Feature Robustness Enhancement Module (FREM), Landmark-aware Objective Function (LOF), and Cobb Angle Calculation Method (CACM), for automated Cobb angle estimation in this paper. To enhance feature extraction, FREM is designed to explore geometric and semantic constraints among landmarks, thus geometric and semantic correlations between landmarks are globally modeled, and robust landmark-based features are extracted. Furthermore, to mitigate the effect of background noise on landmark localization, LOF is proposed to focus more on the foreground near the landmarks and ignore irrelevant background pixels by exploiting category prior information of landmarks. In addition, we also advance CACM to locate the bending segments first and then calculate the Cobb angle within the bending segment, which facilitates the calculation of the clinical standardized Cobb angle. The experiment results on the AASCE dataset demonstrate that our proposed LaNet can significantly improve the Cobb angle estimation performance and outperform other state-of-the-art methods.