Unsupervised feature selection is a challenging task to gain relevant features for improving learning performance due to lack of the label information. Traditional unsupervised feature selection methods are often vector-based, which may ignore the location information of original matrix element. In this paper, we propose a joint sparse matrix regression and nonnegative spectral analysis model for two-dimensional unsupervised feature selection. To obtain proper label information under unsupervised condition, we adopt a nonnegative spectral clustering technique to yield the clustering labels as the pseudo class labels. To directly select the relevant feature on matrix data, we construct a regression relationship between matrix data and the pseudo class labels by deploying left and right regression matrices. Our proposed method can integrate the merits of both sparse matrix regression and nonnegative spectral clustering for feature selection. An efficient optimization algorithm is designed to solve our proposed optimization problem. Extensive experimental results on clustering and classification demonstrate the effectiveness of our proposed method.