Semi-supervised feature extraction has emerged as a highly compelling topic in machine learning fields. However, many existing researches have been introduced based on the Linear Discriminant Analysis (LDA) technique. Therefore, these methods inherited the limitations of LDA and the neighborhood structure of the data can not be well captured. To address these issues, we propose a novel semi-supervised feature extraction method based on adaptive spherical structure detection and inter-class margin maximization. This method transforms samples into a convex spherical structure, maximizing the inter-class margin in the formed convex sphere for all samples. In this way, the intra-class divergence is minimized. At the same time, it mines the local manifold structure of low-dimensional projected data to well characterize the neighborhood relationship between samples. An alternative minimization algorithm is put forward to address the proposed model. Extensive experiments conducted on substantial real-world datasets exhibit that our approach surpasses the related state-of-the-art semi-supervised methods.