Low-rank sparse regression models have been widely adopted in face recognition due to their robustness against occlusion and illumination variations. However, existing methods often suffer from insufficient feature representation and limited modeling of structured corruption across samples. To address these issues, this paper proposes a Hybrid second-order gradient Histogram based Global Low-Rank Sparse Regression (H2H-GLRSR) model. First, we propose the Histogram of Oriented Hessian (HOH) to capture second-order geometric characteristics such as curvature and ridge patterns. By fusing HOH and first-order gradient histograms, we construct a unified local descriptor, termed the Hybrid second-order gradient Histogram (H2H), which enhances structural discriminability under challenging conditions. Subsequently, the H2H features are incorporated into an extended version of the Sparse Regularized Nuclear Norm based Matrix Regression (SR\_NMR) model, where a global low-rank constraint is imposed on the residual matrix to exploit cross-sample correlations in structured noise. The resulting H2H-GLRSR model achieves superior discrimination and robustness. Experimental results on benchmark datasets demonstrate that the proposed method significantly outperforms state-of-the-art regression-based classifiers in both recognition accuracy and computational efficiency.