Significant attention to multiple kernel graph-based clustering (MKGC) has emerged in recent years, primarily due to the superiority of multiple kernel learning (MKL) and the outstanding performance of graph-based clustering. However, many existing MKGC methods design a fat model that poses challenges for computational cost and clustering performance, as they learn both an affinity graph and an extra consensus kernel cumbersomely. To tackle this challenging problem, this article proposes a new MKGC method to learn a consensus affinity graph directly. By using the self-expressiveness graph learning and an adaptive local structure learning term, the local manifold structure of the data in kernel space is preserved for learning multiple candidate affinity graphs from a kernel pool first. After that, these candidate affinity graphs are synthesized to learn a consensus affinity graph via a thin autoweighted fusion model, in which a self-tuned Laplacian rank constraint and a top- k neighbors sparse strategy are introduced to improve the quality of the consensus affinity graph for accurate clustering purposes. The experimental results on ten benchmark datasets and two synthetic datasets show that the proposed method consistently and significantly outperforms the state-of-the-art methods.