To solve the nonlinear unmixing problem of hyperspectral remote sensing images， a multi-graph regularized multi-kernel nonnegative matrix factorization （MGMKNMF） method is proposed， and the multi-graph regularization term in multi-kernel space is constructed. Moreover， the MGMKNMF objective function， which includes multi-graph in multi-kernel regularization， multi-kernel weights regularization， and multi-graph weights regularization terms， is constructed. MGMKNMF can update the multi-kernel and multi-graph weights during the process of learning endmembers and abundance， and precisely construct the graph of the input data in the appropriate multi-kernel space， thereby solving the problem of selecting the graph and kernel weights. Compared with the single kernel function used in kernel nonnegative matrix factorization （KNMF）， multiple kernel functions can determine a more appropriate kernel space. Further， compared with the single graph in graph regularized nonnegative matrix factorization （GNMF）， multiple graphs describe the relationship between samples in different ways， which is more accurate and reliable than the single graph. The experimental results with two real measured datasets and two simulated datasets show that the presented MGMKNMF algorithm is effective. Compared with GNMF， non-pure pixels kernel nonnegative matrix factorization kernel sparse non-negative matrix factorization， kernel-based nonlinear spectral unmixing with dictionary pruning methods， and multi-graph regularized kernel nonnegative matrix factorization method， the average spectral angle distance （SAD） values of the proposed MGMKNMF are the best， that is， 0.092 1 and 0.097 0 on the real Cuprite dataset and Jasper ridge dataset， respectively. The average SAD values of MGMKNMF on the Hapke and generalized bilinear model simulated datasets are 0.137 5 and 0.145 6， respectively. Finally， the root mean square error values are 0.050 6 and 0.057 0， respectively.