Spectral feature selection identifies relevant features by measuring their capability of preserving sample similarity. It provides a powerful framework for both supervised and unsupervised feature selection, and has been proven to be effective in many real-world applications. One common drawback associated with most existing spectral feature selection algorithms is that they evaluate features individually and cannot identify redundant features. Since redundant features can have significant adverse effect on learning performance, it is necessary to address this limitation for spectral feature selection. To this end, we propose a novel spectral feature selection algorithm to handle feature redundancy, adopting an embedded model. The algorithm is derived from a formulation based on a sparse multi-output regression with a L2,1-norm constraint. We conduct theoretical analysis on the properties of its optimal solutions, paving the way for designing an efficient path-following solver. Extensive experiments show that the proposed algorithm can do well in both selecting relevant features and removing redundancy.