For the performance degradation problem of broad learning system (BLS) in non-Gaussian noise environment, the variant of BLS based on M-estimator shows good robust performance. However, in most cases, the determination of the optimal loss function is often very time-consuming due to the lack of prior knowledge of the sample data. Therefore, this paper constructs a variant of BLS based on adaptive robust kernel (AR-BLS) to improve the generalization performance of the model in non-Gaussian noise environment. Adaptive robust kernel function is a general loss function that includes many common M-estimator paradigms. By alternately optimizing model weights and adaptive robust kernel parameters, AR-BLS realizes the adaptive adjustment of model robustness under different outlier noise distributions without human intervention. In addition, the iterative convergence of AR-BLS algorithm is proved based on Zangwill's global convergence theorem. Simulation experiments on multiple public datasets and actual application scenarios verify the effectiveness of the proposed method.