Summary: A nonlinear unmixing algorithm for hyperspectral images based on kernel nonnegative matrix factorization with constraints on abundances is proposed in this paper. The original hyperspectral image data are mapped into a high-dimensional feature space through a kernel function, enabling the nonlinear data become linearly separable in high-dimensional feature space. Then, linear nonnegative matrix factorization is applied for unsupervised hyperspectral unmixing in the high-dimensional feature space. Furthermore, sparseness and smoothness constraints are added on abundances according to the spatial characteristics of the distribution of ground objects. Experimental results on simulated and real hyperspectral data indicate that, compared to other unmixing methods, the proposed algorithm has considered the distribution characteristics of ground objects and can improve the unmixing accuracy in different nonlinear mixing scenarios.