The space resolution of hyperspectral image is influenced due to the restriction of sensor platform, which results in more than one material in one pixel. Such kind of pixel is called mixed pixel. The existence of mixed pixels restricts accurate analysis and application of hyperspectral images. Hyperspectralunmixing technique can factorize mixed pixels to pure material signatures (endmembers) and corresponding proportion (abundance), which makes more accurate material signature available. Unmxing is very important to accurate classification and identification, anomaly detection and quantitative analysis for hyperspectral imagery. Based on linear spectral mixing model, this paper develops an endmember and abundance sparse constrained graph regularized nonnegative matrix factorization (EAGLNMF) algorithm for hyperspectral imagery unmixing. The algorithm is based on nonnegative matrix factorization, and integrates graph regularization and both endmember and abundance sparse constraints to the object function. Graph regularization is used to consider the geometrical structure of the hyperspectral image and sparse constraints can demonstrate the inner manifoldstructure. First, the lost function of EAGLNMF is constructed, and VCA-FCLS method is used as initial value. And then, the value of the parameters is set, including weighting matrix of graph regularization, sparse factors for both endmember signature matrix and abundance matrix. At last, the iteration equations for endmember matrix and abundance matrix are both obtained, and stopping criteria is given. The algorithm does not require pure pixel in the hyperspectral image. In fact, there are little pure pixel in real hyperspectral imagerydue to the sensors platform. Thus, EAGLNMF algorithm provides a kind of solution for real hyperspectral imagery. The availability and effect of EAGLNMF are verified by synthetic data via four experiments. The experiments compare EAGLNMF with VCA-FCLS, standard NMF and GLNMF. Two metrics, spectral angle distance (SAD) and abundance angle distance (AAD) are used to compare the four methods. Experiment 1 is total comparison experiment of the four methods. SNR and the number of endmembers are constant, and the value of SAD and AAD are compared. Experiment 2 evaluates the influence of SNR. Different value for SNR and constant value for number of endmembers are given to different runs. Experiment 3 evaluates the influence of number of endmembers. Different value for number of endmembers and constant value for SNR are given to different runs. The experiment result shows that EAGLNMF method obtains more accurate result for both endmebers and abundance. Moreover, experiment 4 evaluates the influence of sparse factor between endmember signature and abundance. The result demonstrates that endmember sparse constraint shows a positive effect to unmixing. And, sparse factor between endmember signature and abundance shows effect to unmixing result. In addition, real AVIRIS hyperspectral image is applied to VCA-FCLS, standard NMF, GLNMF and the proposed EAGLNMF, and compared with the ground truth of USGS, the result shows that EAGLNMF obtains best unmixing result among the four algorithms and the accuracy of the estimated endmembers is good.