High-dimensional multilabel data have increasingly emerged in many application areas, suffering from two noteworthy issues: instances with high-dimensional features and large-scale labels. Multilabel feature selection methods are widely studied to address the issues. Previous multilabel feature selection methods focus on exploring label correlations to guide the feature selection process, ignoring the impact of latent feature structure on label correlations. In addition, one encouraging property regarding correlations between features and labels is that similar features intend to share similar labels. To this end, a latent structure shared (LSS) term is designed, which shares and preserves both latent feature structure and latent label structure. Furthermore, we employ the graph regularization technique to guarantee the consistency between original feature space and latent feature structure space. Finally, we derive the shared latent feature and label structure feature selection (SSFS) method based on the constrained LSS term, and then, an effective optimization scheme with provable convergence is proposed to solve the SSFS method. Better experimental results on benchmark datasets are achieved in terms of multiple evaluation criteria.