Unsupervised Feature Selection (UFS) methods try to extract features that can well keep the intrinsic structure of data. To make full use of such information in this paper we use one of the simplest graph sparsification strategies MST (Minimum Spanning Tree) for the task of UFS. A novel graph structural information method is proposed for unsupervised feature selection, we simplify and preserve correlation between features via MST through a structure that simultaneously captures the local and global structure of data, and then use graph structural information directly to achieve the subset representative features with minimum redundancy and more discriminative power. To show the effectiveness of our method, some of the most representative and referenced UFS methods are used for conducting experiments on some benchmark datasets. Experimental results verify that the proposed feature subset selection algorithm is effective, more specifically at the running time.