Abstract Multiple kernel clustering (MKC) algorithms usually learn an optimal kernel from a group of pre-specified base kernels to improve the clustering performance. However, we observe that existing MKC algorithms do not well handle the situation that kernels are corrupted with noise and outliers. In this paper, we first propose a novel method to learn an optimal consensus kernel from a group of pre-specified kernel matrices, each of which can be decomposed into the optimal consensus kernel matrix and a sparse error matrix. Further, we propose a scheme to address the problem of considerable corrupted kernels, where each given kernel is adaptively adjusted according to its corresponding error matrix. The inexact augmented Lagrange multiplier scheme is developed for solving the corresponding optimization problem, where the optimal consensus kernel and the localized weight variables are jointly optimized. Extensive experiments well demonstrate the effectiveness and robustness of the proposed algorithm.