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With the enormous amount of multi-source data produced by various sensors and feature extraction approaches, multi-view clustering (MVC) has attracted developing research attention and is widely exploited in data analysis. Most of the existing multi-view clustering methods hold on the assumption that all of the views are complete. However, in many real scenarios, multi-view data are often incomplete for many reasons, e.g., hardware failure or incomplete data collection. In this paper, we propose an adaptive weighted graph fusion incomplete multi-view subspace clustering (AWGF-IMSC) method to solve the incomplete multi-view clustering problem. Firstly, to eliminate the noise existing in the original space, we transform complete original data into latent representations which contribute to better graph construction for each view. Then, we incorporate feature extraction and incomplete graph fusion into a unified framework, whereas two processes can negotiate with each other, serving for graph learning tasks. A sparse regularization is imposed on the complete graph to make it more robust to the view-inconsistency. Besides, the importance of different views is automatically learned, further guiding the construction of the complete graph. An effective iterative algorithm is proposed to solve the resulting optimization problem with convergence. Compared with the existing state-of-the-art methods, the experiment results on several real-world datasets demonstrate the effectiveness and advancement of our proposed method. [ABSTRACT FROM AUTHOR]