Microarray data, when coupled with advanced computational and statistical techniques, offers profound insights into cause of diseases and personalized therapy. However, the enormous genes present in microarray data poses challenges for identifying relevant gene selection, especially in limited labeled dataset. Conventional methods for graph construction suffer from empirical parameter selection, potentially failing to capture intrinsic data properties. To address these issues, we introduce the semi-supervised Adaptive Graph-based Manifold Learning Gene Selection (AGMLGS) approach. This unified framework integrates graph construction and projection matrix learning, preserving high-dimensional data structure (in particular for gene data) in a lower-dimensional space without losing their physical meaning. Our method surpasses seven state-of-the-art algorithms across nine datasets, proving its effectiveness in terms of average precision and exhibiting reasonable computational efficiency in the majority of cases. The MATLAB code employed in the proposed AGMLGS model are accessible in the following URL https://github.com/ml-lab-sau/AGMLGS .