The current graph-based multiple kernel clustering usually adopts a linearly weighted strategy, which limits the representational capacity of the consensus kernel and ignores noise pollution in Reproducing Kernel Hilbert Space (RKHS).To solve the problem, a Robust Self-weighted Multiple Kernel Learning (RSMKL) graph-based subspace clustering algorithm is proposed, which is aimed at enhancing the representational capacity of the kernel and improving the robustness to noise in RKHS.This algorithm adopts a novel nonlinear self-weighted kernel fusion strategy to generate the optimal consensus kernel, and then uses Low-Rank Representation (LRR) in RKHS to remove the influence of noise on the quality of affinity graphs.Finally, an alternating direction method of multipliers with iterative optimization is proposed to solve the objective function.The experimental results on five common data sets show that, compared with five popular homogeneous algorithms, RSMKL possesses better clustering performance on the indexes of ACC, NMI and Purity.