In image analysis, image samples from multiple sources may contain noisy features. Due to the difficulty of obtaining label information and complex intrinsic structures, performing unsupervised feature selection on multi-view data is a challenging problem. Most existing unsupervised multi-view feature selection methods may explore only the inter-view correlations at the view-level, and ignore the explicit correlations between features across multiple views. In this paper, we propose a tensor-based unsupervised multi-view feature selection (TUFS) method. Specifically, TUFS efficiently explores the full-order interactions among multi-view data without physically building a tensor. Besides, multiple local geometric structures for different views are constructed to facilitate unsupervised feature selection. To solve the proposed model, we design an alternating optimization algorithm. Experiments and comparisons on three image datasets demonstrate that the proposed TUFS yields better performance over the state-of-the-art methods.