Incomplete multi-view clustering aims to cluster samples with missing views, which has drawn more and more research interest. Although several methods have been developed for incomplete multi-view clustering, they fail to extract and exploit the comprehensive global and local structure of multi-view data, so their clustering performance is limited. This paper proposes a Clustering-induced Adaptive Structure Enhancing Network (CASEN) for incomplete multi-view clustering, which is an end-to-end trainable framework that jointly conducts multi-view structure enhancing and data clustering. Our method adopts multi-view autoencoder to infer the missing features of the incomplete samples. Then, we perform adaptive graph learning and graph convolution on the reconstructed complete multi-view data to effectively extract data structure. Moreover, we use multiple kernel clustering to integrate the global and local structure for clustering, and the clustering results in turn are used to enhance the data structure. Extensive experiments on several benchmark datasets demonstrate that our method can comprehensively obtain the structure of incomplete multi-view data and achieve superior performance compared to the other methods.