Graph-based multi-view clustering is one of the representative methods in that field. However, existing models still have problems as following. First, most of them do not consider the difference of clustering capacity among different views and force all views to share a common similarity graph. Next, some models construct the similarity graph and conduct clustering in separated steps, resulting in the constructed similarity graph is not optimal for the following clustering tasks. Finally, although there are many models using kernel learning to deal with the nonlinear relationship between data points, most of them calculate the self-expressive relationship in kernel space based on global models. Such global schemes are not conducive to fully explore local nonlinear relationship, and easy to bring about heavy computing load. Therefore, this paper proposes a late fusion multi-view clustering model based on local multi-kernel learning. We implement information fusion at the level of class partition space rather than similarity graph, and adopt local multi-kernel learning scheme to fully preserve the local nonlinear relationship as well as reduce the computational load. We also propose an alternative optimization scheme to solve the construction of similarity graph, combination of multi-kernel and generation of class indicator matrix in a unified framework. Experiments on multiple datasets show that the proposed method has good multi-view clustering effect.