Current existing clustering methods for handling incomplete multi-view data primarily concentrate on learning a common representation or graph from the available views, while overlooking the latent information contained in the missing views and the imbalance of information among different views. Furthermore, instances with weak discriminative features usually degrading the precision of consistent representation or graph across all views. To address these problems, in this paper, we propose a simple but efficient method, called high-confident local structure guided consensus graph learning for incomplete multi-view clustering (HLSCG_IMC). Specifically, this method can adaptively learn a strict block diagonal structure from the available samples using a block diagonal representation regularizer. Different from the existing methods using a simple pairwise affinity graph for structure construction, we consider the influence of instances located at the edge of two clusters on the construction of graph for each view. By harnessing the proposed high-confident strict block diagonal structures, the approach seeks to directly guide the learning of the robust consensus graph. A number of experiments have been conducted to verify the efficacy of our approach.