Traditional graph embedding methods often use single graph structures for feature extraction (FE).However, these methods cannot effectively represent the complex intrinsic structuresof high-dimensional data. To address this problem, a Semi-Supervised Multi-Graph Embedding (SSMGE) algorithm was proposed for FE of Hyper Spectral Images (HSIs). First, the SSMGE method constructed one of each of intra-and inter-class hypergraphs and intra-and inter-class graphs through intra-and inter-class neighbors of labeled samples.In addition, it constructs an unsupervised intrinsic hypergraph and a penalty hypergraph using unlabeled samples. The fusion of graphs and hypergraphs can effectively characterize the complex relationships in high-dimensional data. The SSMGE method not only effectively reveals the intrinsic structure of an HSI by exploring the collaboration of graphs and hypergraphs but also enhances the discriminative ability of extracted features in low-dimensional embedding space.This enables improved classification performance of HSI data. Experimental results on the PaviaU and Urban hyperspectral datasets show that the overall accuracies of the proposed method reached 85.92% and 79.74%, respectively. The SSMGE method can significantly improve classification performance as compared with some state-of-the-art FE methods.