Incomplete multi-view clustering which aims to solve the difficult clustering challenge on incomplete multi-view data collected from diverse domains with missing views has drawn considerable attention in recent years. In this paper, we propose a novel method, called consensus guided incomplete multi-view spectral clustering (CGIMVSC), to address the incomplete clustering problem. Specifically, CGIMVSC seeks to explore the local information within every single-view and the semantic consistent information shared by all views in a unified framework simultaneously, where the local structure is adaptively obtained from the incomplete data rather than pre-constructed via a k-nearest neighbor approach in the existing methods. Considering the semantic consistency of multiple views, CGIMVSC introduces a co-regularization constraint to minimize the disagreement between the common representation and the individual representations with respect to different views, such that all views will obtain a consensus clustering result. Experimental comparisons with some state-of-the-art methods on seven datasets validate the effectiveness of the proposed method on incomplete multi-view clustering.