In order to analyze hyperspectral images consisted of highly mixed pixels, a new endmembers overall coverage constraint was proposed and introduced in objective function of nonnegative matrix factorization, which forcely maximizes the number of pixels contained in the simplex constructed by endmembers using data geometrical properties in the feature space while satisfies data nonnegative and abundance sum-to-one constraint simultaneously. In the maximum overall coverage constraint nonnegative matrix factorization algorithm, the dimensionality reduction process is prevented to preserve the physical meaning of the source image and multiplicative update rules are applied to avoid stepsize selection problem occurred in traditional gradient-based optimization algorithm frequently. To evaluate the accuracy of endmembers extraction, the performance and robustness, experiments are designed on synthetic and real images. The results demonstrate that the proposed algorithm is an effective method to analyze mixed data in hyperspectral image.