The explosion of information has been evoking a leading wave of big data research during recent years. Despite many empirical successes of spectral clustering algorithms, it is still challenging to cluster the high dimensional data due to the curse of dimensionality. This study proposes a novel algorithm referred to as joint Laplacian regularization and adaptive feature learning (LRAFL), which adaptively learns the feature weights and fits the feature selection as well as clustering into a unified framework, rather than the two-phase strategy of typical approaches. With a new rank constraint imposed on the Laplacian matrix, the connected components in the resulted similarity matrix are exactly equal to the cluster number. An effective approach is also proposed to solve the formulated optimization problem. Comprehensive analyses, including convergence behavior, computational complexity, and together with parameter determination are also presented. Surprisingly sound experimental results can be achieved on synthetic data and benchmark datasets by the proposed algorithm when compared with the related state-of-the-art clustering approaches.