Unsupervised feature selection is a useful tool for reducing the complexity and improving the generalization performance of data mining tasks. In this paper, we propose an Adaptive Unsupervised Feature Selection (AUFS) algorithm with explicit l2/l0-norm minimization. We use a joint adaptive loss for data fitting and a l2/l0 minimization for feature selection. We solve the optimization problem with an efficient iterative algorithm and prove that all the expected properties of unsupervised feature selection can be preserved. We also show that the computational complexity and memory use is only linear to the number of instances and square to the number of clusters. Experiments show that our algorithm outperforms the state-of-the-arts on seven different benchmark data sets.